En C/C++ el número de dígitos que puede tener un int largo es un máximo de 20. Y la cuestión es almacenar el número de 22 dígitos que no es fácil de almacenar en ningún tipo primitivo. Entonces, para lidiar con este tipo de problema, diseñemos un nuevo tipo de datos que se llamará BigInt. En este artículo, se implementarán algunas operaciones básicas en el nuevo tipo de datos.
- Suma dos números enteros grandes.
- Restar dos números enteros grandes
- Multiplica dos enteros grandes.
- Divide dos enteros grandes.
- Modulo dos enteros grandes
- Elevar un entero grande a una potencia
- La raíz cuadrada de un entero grande
- Comparación entre dos números enteros grandes para comprobar cuál es mayor y cuál es menor.
- Encuentra el número de dígitos en el entero grande.
- Imprime el entero grande.
- Convierte un entero en un entero grande.
Aplicaciones de BigInt:
a continuación se muestran algunas aplicaciones básicas del nuevo tipo de datos, BigInt:
- Cálculo del número de Fibonacci de un número grande.
- Cálculo del número catalán de un número grande
- Cálculo del Factorial de un entero grande.
Enfoque:
Para crear un nuevo tipo de datos de números enteros grandes, se están implementando los siguientes conceptos:
- Strings C++ en las que podemos almacenar nuestros números en forma de caracteres (en orden inverso para fines de eficiencia) de modo que al usar strings también podemos almacenar números muy grandes.
- Para la operación de suma/resta de dos números enteros grandes, use la matemática básica para la suma que dice que sume los dos dígitos correspondientes y, si se genera algún acarreo, súmelo a la suma de los siguientes dígitos y repita este proceso hasta que se sumen todos los dígitos. sustraído
- De manera similar, para la multiplicación de dos números, use el enfoque matemático básico que establece que multiplique cada dígito de un número con el otro número completo y, por último, sume todos los números que obtenga en la multiplicación.
- Las siguientes operaciones se están realizando en BigInt-
- Definición de algunos números enteros grandes.
- Comprobación del número de dígitos en el entero grande.
- Post/Pre Incremento o Decremento
- Sumar dos números enteros grandes.
- Restar dos números enteros grandes.
- Multiplicar dos números enteros grandes.
- Dividir dos enteros grandes
- Módulo de dos enteros grandes
- La raíz cuadrada de un entero grande (valor entero inferior)
- Elevar un entero grande a una potencia
- Convertir un entero simple en un entero grande.
- Cálculo de Fibonacci hasta 10 000. (incluso 100000 pero más lento)
- Cálculo de Factoriales hasta 1 000.
- Cálculo del catalán hasta 1 000.
- Comprobar qué entero grande es mayor y cuál es menor.
A continuación se muestra la implementación en C++ del enfoque anterior:
C++
// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
class BigInt{
string digits;
public:
//Constructors:
BigInt(unsigned long long n = 0);
BigInt(string &);
BigInt(const char *);
BigInt(BigInt &);
//Helper Functions:
friend void divide_by_2(BigInt &a);
friend bool Null(const BigInt &);
friend int Length(const BigInt &);
int operator[](const int)const;
/* * * * Operator Overloading * * * */
//Direct assignment
BigInt &operator=(const BigInt &);
//Post/Pre - Incrementation
BigInt &operator++();
BigInt operator++(int temp);
BigInt &operator--();
BigInt operator--(int temp);
//Addition and Subtraction
friend BigInt &operator+=(BigInt &, const BigInt &);
friend BigInt operator+(const BigInt &, const BigInt &);
friend BigInt operator-(const BigInt &, const BigInt &);
friend BigInt &operator-=(BigInt &, const BigInt &);
//Comparison operators
friend bool operator==(const BigInt &, const BigInt &);
friend bool operator!=(const BigInt &, const BigInt &);
friend bool operator>(const BigInt &, const BigInt &);
friend bool operator>=(const BigInt &, const BigInt &);
friend bool operator<(const BigInt &, const BigInt &);
friend bool operator<=(const BigInt &, const BigInt &);
//Multiplication and Division
friend BigInt &operator*=(BigInt &, const BigInt &);
friend BigInt operator*(const BigInt &, const BigInt &);
friend BigInt &operator/=(BigInt &, const BigInt &);
friend BigInt operator/(const BigInt &, const BigInt &);
//Modulo
friend BigInt operator%(const BigInt &, const BigInt &);
friend BigInt &operator%=(BigInt &, const BigInt &);
//Power Function
friend BigInt &operator^=(BigInt &,const BigInt &);
friend BigInt operator^(BigInt &, const BigInt &);
//Square Root Function
friend BigInt sqrt(BigInt &a);
//Read and Write
friend ostream &operator<<(ostream &,const BigInt &);
friend istream &operator>>(istream &, BigInt &);
//Others
friend BigInt NthCatalan(int n);
friend BigInt NthFibonacci(int n);
friend BigInt Factorial(int n);
};
BigInt::BigInt(string & s){
digits = "";
int n = s.size();
for (int i = n - 1; i >= 0;i--){
if(!isdigit(s[i]))
throw("ERROR");
digits.push_back(s[i] - '0');
}
}
BigInt::BigInt(unsigned long long nr){
do{
digits.push_back(nr % 10);
nr /= 10;
} while (nr);
}
BigInt::BigInt(const char *s){
digits = "";
for (int i = strlen(s) - 1; i >= 0;i--)
{
if(!isdigit(s[i]))
throw("ERROR");
digits.push_back(s[i] - '0');
}
}
BigInt::BigInt(BigInt & a){
digits = a.digits;
}
bool Null(const BigInt& a){
if(a.digits.size() == 1 && a.digits[0] == 0)
return true;
return false;
}
int Length(const BigInt & a){
return a.digits.size();
}
int BigInt::operator[](const int index)const{
if(digits.size() <= index || index < 0)
throw("ERROR");
return digits[index];
}
bool operator==(const BigInt &a, const BigInt &b){
return a.digits == b.digits;
}
bool operator!=(const BigInt & a,const BigInt &b){
return !(a == b);
}
bool operator<(const BigInt&a,const BigInt&b){
int n = Length(a), m = Length(b);
if(n != m)
return n < m;
while(n--)
if(a.digits[n] != b.digits[n])
return a.digits[n] < b.digits[n];
return false;
}
bool operator>(const BigInt&a,const BigInt&b){
return b < a;
}
bool operator>=(const BigInt&a,const BigInt&b){
return !(a < b);
}
bool operator<=(const BigInt&a,const BigInt&b){
return !(a > b);
}
BigInt &BigInt::operator=(const BigInt &a){
digits = a.digits;
return *this;
}
BigInt &BigInt::operator++(){
int i, n = digits.size();
for (i = 0; i < n && digits[i] == 9;i++)
digits[i] = 0;
if(i == n)
digits.push_back(1);
else
digits[i]++;
return *this;
}
BigInt BigInt::operator++(int temp){
BigInt aux;
aux = *this;
++(*this);
return aux;
}
BigInt &BigInt::operator--(){
if(digits[0] == 0 && digits.size() == 1)
throw("UNDERFLOW");
int i, n = digits.size();
for (i = 0; digits[i] == 0 && i < n;i++)
digits[i] = 9;
digits[i]--;
if(n > 1 && digits[n - 1] == 0)
digits.pop_back();
return *this;
}
BigInt BigInt::operator--(int temp){
BigInt aux;
aux = *this;
--(*this);
return aux;
}
BigInt &operator+=(BigInt &a,const BigInt& b){
int t = 0, s, i;
int n = Length(a), m = Length(b);
if(m > n)
a.digits.append(m - n, 0);
n = Length(a);
for (i = 0; i < n;i++){
if(i < m)
s = (a.digits[i] + b.digits[i]) + t;
else
s = a.digits[i] + t;
t = s / 10;
a.digits[i] = (s % 10);
}
if(t)
a.digits.push_back(t);
return a;
}
BigInt operator+(const BigInt &a, const BigInt &b){
BigInt temp;
temp = a;
temp += b;
return temp;
}
BigInt &operator-=(BigInt&a,const BigInt &b){
if(a < b)
throw("UNDERFLOW");
int n = Length(a), m = Length(b);
int i, t = 0, s;
for (i = 0; i < n;i++){
if(i < m)
s = a.digits[i] - b.digits[i]+ t;
else
s = a.digits[i]+ t;
if(s < 0)
s += 10,
t = -1;
else
t = 0;
a.digits[i] = s;
}
while(n > 1 && a.digits[n - 1] == 0)
a.digits.pop_back(),
n--;
return a;
}
BigInt operator-(const BigInt& a,const BigInt&b){
BigInt temp;
temp = a;
temp -= b;
return temp;
}
BigInt &operator*=(BigInt &a, const BigInt &b)
{
if(Null(a) || Null(b)){
a = BigInt();
return a;
}
int n = a.digits.size(), m = b.digits.size();
vector<int> v(n + m, 0);
for (int i = 0; i < n;i++)
for (int j = 0; j < m;j++){
v[i + j] += (a.digits[i] ) * (b.digits[j]);
}
n += m;
a.digits.resize(v.size());
for (int s, i = 0, t = 0; i < n; i++)
{
s = t + v[i];
v[i] = s % 10;
t = s / 10;
a.digits[i] = v[i] ;
}
for (int i = n - 1; i >= 1 && !v[i];i--)
a.digits.pop_back();
return a;
}
BigInt operator*(const BigInt&a,const BigInt&b){
BigInt temp;
temp = a;
temp *= b;
return temp;
}
BigInt &operator/=(BigInt& a,const BigInt &b){
if(Null(b))
throw("Arithmetic Error: Division By 0");
if(a < b){
a = BigInt();
return a;
}
if(a == b){
a = BigInt(1);
return a;
}
int i, lgcat = 0, cc;
int n = Length(a), m = Length(b);
vector<int> cat(n, 0);
BigInt t;
for (i = n - 1; t * 10 + a.digits[i] < b;i--){
t *= 10;
t += a.digits[i] ;
}
for (; i >= 0; i--){
t = t * 10 + a.digits[i];
for (cc = 9; cc * b > t;cc--);
t -= cc * b;
cat[lgcat++] = cc;
}
a.digits.resize(cat.size());
for (i = 0; i < lgcat;i++)
a.digits[i] = cat[lgcat - i - 1];
a.digits.resize(lgcat);
return a;
}
BigInt operator/(const BigInt &a,const BigInt &b){
BigInt temp;
temp = a;
temp /= b;
return temp;
}
BigInt &operator%=(BigInt& a,const BigInt &b){
if(Null(b))
throw("Arithmetic Error: Division By 0");
if(a < b){
a = BigInt();
return a;
}
if(a == b){
a = BigInt(1);
return a;
}
int i, lgcat = 0, cc;
int n = Length(a), m = Length(b);
vector<int> cat(n, 0);
BigInt t;
for (i = n - 1; t * 10 + a.digits[i] < b;i--){
t *= 10;
t += a.digits[i];
}
for (; i >= 0; i--){
t = t * 10 + a.digits[i];
for (cc = 9; cc * b > t;cc--);
t -= cc * b;
cat[lgcat++] = cc;
}
a = t;
return a;
}
BigInt operator%(const BigInt &a,BigInt &b){
BigInt temp;
temp = a;
temp %= b;
return temp;
}
BigInt &operator^=(BigInt & a,const BigInt & b){
BigInt Exponent, Base(a);
Exponent = b;
a = 1;
while(!Null(Exponent)){
if(Exponent[0] & 1)
a *= Base;
Base *= Base;
divide_by_2(Exponent);
}
return a;
}
BigInt operator^(BigInt & a,BigInt & b){
BigInt temp(a);
temp ^= b;
return temp;
}
void divide_by_2(BigInt & a){
int add = 0;
for (int i = a.digits.size() - 1; i >= 0;i--){
int digit = (a.digits[i] >> 1) + add;
add = ((a.digits[i] & 1) * 5);
a.digits[i] = digit;
}
while(a.digits.size() > 1 && !a.digits.back())
a.digits.pop_back();
}
BigInt sqrt(BigInt & a){
BigInt left(1), right(a), v(1), mid, prod;
divide_by_2(right);
while(left <= right){
mid += left;
mid += right;
divide_by_2(mid);
prod = (mid * mid);
if(prod <= a){
v = mid;
++mid;
left = mid;
}
else{
--mid;
right = mid;
}
mid = BigInt();
}
return v;
}
BigInt NthCatalan(int n){
BigInt a(1),b;
for (int i = 2; i <= n;i++)
a *= i;
b = a;
for (int i = n + 1; i <= 2 * n;i++)
b *= i;
a *= a;
a *= (n + 1);
b /= a;
return b;
}
BigInt NthFibonacci(int n){
BigInt a(1), b(1), c;
if(!n)
return c;
n--;
while(n--){
c = a + b;
b = a;
a = c;
}
return b;
}
BigInt Factorial(int n){
BigInt f(1);
for (int i = 2; i <= n;i++)
f *= i;
return f;
}
istream &operator>>(istream &in,BigInt&a){
string s;
in >> s;
int n = s.size();
for (int i = n - 1; i >= 0;i--){
if(!isdigit(s[i]))
throw("INVALID NUMBER");
a.digits[n - i - 1] = s[i];
}
return in;
}
ostream &operator<<(ostream &out,const BigInt &a){
for (int i = a.digits.size() - 1; i >= 0;i--)
cout << (short)a.digits[i];
return cout;
}
//Driver code with some examples
int main()
{
BigInt first("12345");
cout << "The number of digits"
<< " in first big integer = "
<< Length(first) << '\n';
BigInt second(12345);
if (first == second) {
cout << "first and second are equal!\n";
}
else
cout << "Not equal!\n";
BigInt third("10000");
BigInt fourth("100000");
if (third < fourth) {
cout << "third is smaller than fourth!\n";
}
BigInt fifth("10000000");
if (fifth > fourth) {
cout << "fifth is larger than fourth!\n";
}
// Printing all the numbers
cout << "first = " << first << '\n';
cout << "second = " << second << '\n';
cout << "third = " << third << '\n';
cout << "fourth = " << fourth<< '\n';
cout << "fifth = " << fifth<< '\n';
// Incrementing the value of first
first++;
cout << "After incrementing the"
<< " value of first is : ";
cout << first << '\n';
BigInt sum;
sum = (fourth + fifth);
cout << "Sum of fourth and fifth = "
<< sum << '\n';
BigInt product;
product = second * third;
cout << "Product of second and third = "
<< product << '\n';
// Print the fibonaccii number from 1 to 100
cout << "-------------------------Fibonacci"
<< "------------------------------\n";
for (int i = 0; i <= 100; i++) {
BigInt Fib;
Fib = NthFibonacci(i);
cout << "Fibonacci " << i << " = " << Fib<<'\n';
}
cout << "-------------------------Catalan"
<< "------------------------------\n";
for (int i = 0; i <= 100; i++) {
BigInt Cat;
Cat = NthCatalan(i);
cout << "Catalan " << i << " = " << Cat<<'\n';
}
// Calculating factorial of from 1 to 100
cout << "-------------------------Factorial"
<< "------------------------------\n";
for (int i = 0; i <= 100; i++) {
BigInt fact;
fact = Factorial(i);
cout << "Factorial of "
<< i << " = ";
cout << fact << '\n';
}
// This code is contributed
// by Gatea David
}
Producción
The number of digits in first big integer = 5 first and second are equal! third is smaller than fourth! fifth is larger than fourth! first = 12345 second = 12345 third = 10000 fourth = 100000 fifth = 10000000 After incrementing the value of first is : 12346 Sum of fourth and fifth = 10100000 Product of second and third = 123450000 -------------------------Fibonacci------------------------------ Fibonacci 0 = 0 Fibonacci 1 = 1 Fibonacci 2 = 1 Fibonacci 3 = 2 Fibonacci 4 = 3 Fibonacci 5 = 5 Fibonacci 6 = 8 Fibonacci 7 = 13 Fibonacci 8 = 21 Fibonacci 9 = 34 Fibonacci 10 = 55 Fibonacci 11 = 89 Fibonacci 12 = 144 Fibonacci 13 = 233 Fibonacci 14 = 377 Fibonacci 15 = 610 Fibonacci 16 = 987 Fibonacci 17 = 1597 Fibonacci 18 = 2584 Fibonacci 19 = 4181 Fibonacci 20 = 6765 Fibonacci 21 = 10946 Fibonacci 22 = 17711 Fibonacci 23 = 28657 Fibonacci 24 = 46368 Fibonacci 25 = 75025 Fibonacci 26 = 121393 Fibonacci 27 = 196418 Fibonacci 28 = 317811 Fibonacci 29 = 514229 Fibonacci 30 = 832040 Fibonacci 31 = 1346269 Fibonacci 32 = 2178309 Fibonacci 33 = 3524578 Fibonacci 34 = 5702887 Fibonacci 35 = 9227465 Fibonacci 36 = 14930352 Fibonacci 37 = 24157817 Fibonacci 38 = 39088169 Fibonacci 39 = 63245986 Fibonacci 40 = 102334155 Fibonacci 41 = 165580141 Fibonacci 42 = 267914296 Fibonacci 43 = 433494437 Fibonacci 44 = 701408733 Fibonacci 45 = 1134903170 Fibonacci 46 = 1836311903 Fibonacci 47 = 2971215073 Fibonacci 48 = 4807526976 Fibonacci 49 = 7778742049 Fibonacci 50 = 12586269025 Fibonacci 51 = 20365011074 Fibonacci 52 = 32951280099 Fibonacci 53 = 53316291173 Fibonacci 54 = 86267571272 Fibonacci 55 = 139583862445 Fibonacci 56 = 225851433717 Fibonacci 57 = 365435296162 Fibonacci 58 = 591286729879 Fibonacci 59 = 956722026041 Fibonacci 60 = 1548008755920 Fibonacci 61 = 2504730781961 Fibonacci 62 = 4052739537881 Fibonacci 63 = 6557470319842 Fibonacci 64 = 10610209857723 Fibonacci 65 = 17167680177565 Fibonacci 66 = 27777890035288 Fibonacci 67 = 44945570212853 Fibonacci 68 = 72723460248141 Fibonacci 69 = 117669030460994 Fibonacci 70 = 190392490709135 Fibonacci 71 = 308061521170129 Fibonacci 72 = 498454011879264 Fibonacci 73 = 806515533049393 Fibonacci 74 = 1304969544928657 Fibonacci 75 = 2111485077978050 Fibonacci 76 = 3416454622906707 Fibonacci 77 = 5527939700884757 Fibonacci 78 = 8944394323791464 Fibonacci 79 = 14472334024676221 Fibonacci 80 = 23416728348467685 Fibonacci 81 = 37889062373143906 Fibonacci 82 = 61305790721611591 Fibonacci 83 = 99194853094755497 Fibonacci 84 = 160500643816367088 Fibonacci 85 = 259695496911122585 Fibonacci 86 = 420196140727489673 Fibonacci 87 = 679891637638612258 Fibonacci 88 = 1100087778366101931 Fibonacci 89 = 1779979416004714189 Fibonacci 90 = 2880067194370816120 Fibonacci 91 = 4660046610375530309 Fibonacci 92 = 7540113804746346429 Fibonacci 93 = 12200160415121876738 Fibonacci 94 = 19740274219868223167 Fibonacci 95 = 31940434634990099905 Fibonacci 96 = 51680708854858323072 Fibonacci 97 = 83621143489848422977 Fibonacci 98 = 135301852344706746049 Fibonacci 99 = 218922995834555169026 Fibonacci 100 = 354224848179261915075 -------------------------Catalan------------------------------ Catalan 0 = 1 Catalan 1 = 1 Catalan 2 = 2 Catalan 3 = 5 Catalan 4 = 14 Catalan 5 = 42 Catalan 6 = 132 Catalan 7 = 429 Catalan 8 = 1430 Catalan 9 = 4862 Catalan 10 = 16796 Catalan 11 = 58786 Catalan 12 = 208012 Catalan 13 = 742900 Catalan 14 = 2674440 Catalan 15 = 9694845 Catalan 16 = 35357670 Catalan 17 = 129644790 Catalan 18 = 477638700 Catalan 19 = 1767263190 Catalan 20 = 6564120420 Catalan 21 = 24466267020 Catalan 22 = 91482563640 Catalan 23 = 343059613650 Catalan 24 = 1289904147324 Catalan 25 = 4861946401452 Catalan 26 = 18367353072152 Catalan 27 = 69533550916004 Catalan 28 = 263747951750360 Catalan 29 = 1002242216651368 Catalan 30 = 3814986502092304 Catalan 31 = 14544636039226909 Catalan 32 = 55534064877048198 Catalan 33 = 212336130412243110 Catalan 34 = 812944042149730764 Catalan 35 = 3116285494907301262 Catalan 36 = 11959798385860453492 Catalan 37 = 45950804324621742364 Catalan 38 = 176733862787006701400 Catalan 39 = 680425371729975800390 Catalan 40 = 2622127042276492108820 Catalan 41 = 10113918591637898134020 Catalan 42 = 39044429911904443959240 Catalan 43 = 150853479205085351660700 Catalan 44 = 583300119592996693088040 Catalan 45 = 2257117854077248073253720 Catalan 46 = 8740328711533173390046320 Catalan 47 = 33868773757191046886429490 Catalan 48 = 131327898242169365477991900 Catalan 49 = 509552245179617138054608572 Catalan 50 = 1978261657756160653623774456 Catalan 51 = 7684785670514316385230816156 Catalan 52 = 29869166945772625950142417512 Catalan 53 = 116157871455782434250553845880 Catalan 54 = 451959718027953471447609509424 Catalan 55 = 1759414616608818870992479875972 Catalan 56 = 6852456927844873497549658464312 Catalan 57 = 26700952856774851904245220912664 Catalan 58 = 104088460289122304033498318812080 Catalan 59 = 405944995127576985730643443367112 Catalan 60 = 1583850964596120042686772779038896 Catalan 61 = 6182127958584855650487080847216336 Catalan 62 = 24139737743045626825711458546273312 Catalan 63 = 94295850558771979787935384946380125 Catalan 64 = 368479169875816659479009042713546950 Catalan 65 = 1440418573150919668872489894243865350 Catalan 66 = 5632681584560312734993915705849145100 Catalan 67 = 22033725021956517463358552614056949950 Catalan 68 = 86218923998960285726185640663701108500 Catalan 69 = 337485502510215975556783793455058624700 Catalan 70 = 1321422108420282270489942177190229544600 Catalan 71 = 5175569924646105559418940193995065716350 Catalan 72 = 20276890389709399862928998568254641025700 Catalan 73 = 79463489365077377841208237632349268884500 Catalan 74 = 311496878311103321137536291518809134027240 Catalan 75 = 1221395654430378811828760722007962130791020 Catalan 76 = 4790408930363303911328386208394864461024520 Catalan 77 = 18793142726809884575211361279087545193250040 Catalan 78 = 73745243611532458459690151854647329239335600 Catalan 79 = 289450081175264899454283846029490767264392230 Catalan 80 = 1136359577947336271931632877004667456667613940 Catalan 81 = 4462290049988320482463241297506133183499654740 Catalan 82 = 17526585015616776834735140517915655636396234280 Catalan 83 = 68854441132780194707888052034668647142985206100 Catalan 84 = 270557451039395118028642463289168566420671280440 Catalan 85 = 1063353702922273835973036658043476458723103404520 Catalan 86 = 4180080073556524734514695828170907458428751314320 Catalan 87 = 16435314834665426797069144960762886143367590394940 Catalan 88 = 64633260585762914370496637486146181462681535261000 Catalan 89 = 254224158304000796523953440778841647086547372026600 Catalan 90 = 1000134600800354781929399250536541864362461089950800 Catalan 91 = 3935312233584004685417853572763349509774031680023800 Catalan 92 = 15487357822491889407128326963778343232013931127835600 Catalan 93 = 60960876535340415751462563580829648891969728907438000 Catalan 94 = 239993345518077005168915776623476723006280827488229600 Catalan 95 = 944973797977428207852605870454939596837230758234904050 Catalan 96 = 3721443204405954385563870541379246659709506697378694300 Catalan 97 = 14657929356129575437016877846657032761712954950899755100 Catalan 98 = 57743358069601357782187700608042856334020731624756611000 Catalan 99 = 227508830794229349661819540395688853956041682601541047340 Catalan 100 = 896519947090131496687170070074100632420837521538745909320 -------------------------Factorial------------------------------ Factorial of 0 = 1 Factorial of 1 = 1 Factorial of 2 = 2 Factorial of 3 = 6 Factorial of 4 = 24 Factorial of 5 = 120 Factorial of 6 = 720 Factorial of 7 = 5040 Factorial of 8 = 40320 Factorial of 9 = 362880 Factorial of 10 = 3628800 Factorial of 11 = 39916800 Factorial of 12 = 479001600 Factorial of 13 = 6227020800 Factorial of 14 = 87178291200 Factorial of 15 = 1307674368000 Factorial of 16 = 20922789888000 Factorial of 17 = 355687428096000 Factorial of 18 = 6402373705728000 Factorial of 19 = 121645100408832000 Factorial of 20 = 2432902008176640000 Factorial of 21 = 51090942171709440000 Factorial of 22 = 1124000727777607680000 Factorial of 23 = 25852016738884976640000 Factorial of 24 = 620448401733239439360000 Factorial of 25 = 15511210043330985984000000 Factorial of 26 = 403291461126605635584000000 Factorial of 27 = 10888869450418352160768000000 Factorial of 28 = 304888344611713860501504000000 Factorial of 29 = 8841761993739701954543616000000 Factorial of 30 = 265252859812191058636308480000000 Factorial of 31 = 8222838654177922817725562880000000 Factorial of 32 = 263130836933693530167218012160000000 Factorial of 33 = 8683317618811886495518194401280000000 Factorial of 34 = 295232799039604140847618609643520000000 Factorial of 35 = 10333147966386144929666651337523200000000 Factorial of 36 = 371993326789901217467999448150835200000000 Factorial of 37 = 13763753091226345046315979581580902400000000 Factorial of 38 = 523022617466601111760007224100074291200000000 Factorial of 39 = 20397882081197443358640281739902897356800000000 Factorial of 40 = 815915283247897734345611269596115894272000000000 Factorial of 41 = 33452526613163807108170062053440751665152000000000 Factorial of 42 = 1405006117752879898543142606244511569936384000000000 Factorial of 43 = 60415263063373835637355132068513997507264512000000000 Factorial of 44 = 2658271574788448768043625811014615890319638528000000000 Factorial of 45 = 119622220865480194561963161495657715064383733760000000000 Factorial of 46 = 5502622159812088949850305428800254892961651752960000000000 Factorial of 47 = 258623241511168180642964355153611979969197632389120000000000 Factorial of 48 = 12413915592536072670862289047373375038521486354677760000000000 Factorial of 49 = 608281864034267560872252163321295376887552831379210240000000000 Factorial of 50 = 30414093201713378043612608166064768844377641568960512000000000000 Factorial of 51 = 1551118753287382280224243016469303211063259720016986112000000000000 Factorial of 52 = 80658175170943878571660636856403766975289505440883277824000000000000 Factorial of 53 = 4274883284060025564298013753389399649690343788366813724672000000000000 Factorial of 54 = 230843697339241380472092742683027581083278564571807941132288000000000000 Factorial of 55 = 12696403353658275925965100847566516959580321051449436762275840000000000000 Factorial of 56 = 710998587804863451854045647463724949736497978881168458687447040000000000000 Factorial of 57 = 40526919504877216755680601905432322134980384796226602145184481280000000000000 Factorial of 58 = 2350561331282878571829474910515074683828862318181142924420699914240000000000000 Factorial of 59 = 138683118545689835737939019720389406345902876772687432540821294940160000000000000 Factorial of 60 = 8320987112741390144276341183223364380754172606361245952449277696409600000000000000 Factorial of 61 = 507580213877224798800856812176625227226004528988036003099405939480985600000000000000 Factorial of 62 = 31469973260387937525653122354950764088012280797258232192163168247821107200000000000000 Factorial of 63 = 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000 Factorial of 64 = 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 Factorial of 65 = 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000 Factorial of 66 = 544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000 Factorial of 67 = 36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000 Factorial of 68 = 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000 Factorial of 69 = 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000 Factorial of 70 = 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000 Factorial of 71 = 850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000 Factorial of 72 = 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000 Factorial of 73 = 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000 Factorial of 74 = 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000 Factorial of 75 = 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000 Factorial of 76 = 1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000 Factorial of 77 = 145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000 Factorial of 78 = 11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000 Factorial of 79 = 894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000 Factorial of 80 = 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000 Factorial of 81 = 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000 Factorial of 82 = 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000 Factorial of 83 = 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000 Factorial of 84 = 3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000 Factorial of 85 = 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000 Factorial of 86 = 24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000 Factorial of 87 = 2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000 Factorial of 88 = 185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000 Factorial of 89 = 16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000 Factorial of 90 = 1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000 Factorial of 91 = 135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000 Factorial of 92 = 12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000 Factorial of 93 = 1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000 Factorial of 94 = 108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000 Factorial of 95 = 10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000 Factorial of 96 = 991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000 Factorial of 97 = 96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000 Factorial of 98 = 9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000 Factorial of 99 = 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000 Factorial of 100 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
Publicación traducida automáticamente
Artículo escrito por abhishek005 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA