Dado un número grande, la tarea es verificar si el número es divisible por 13 o no.
Ejemplos:
Input : 637 Output : 637 is divisible by 13. Input : 920 Output : 920 is not divisible by 13. Input : 83959092724 Output : 83959092724 is divisible by 13.
Si el número num dado es pequeño, podemos encontrar fácilmente si es divisible por 13 o no haciendo num % 13 y verificando si el resultado es 0 o no. Pero ¿qué pasa con los números muy grandes. Hablemos de grandes números.
A continuación se presentan algunos datos interesantes sobre la divisibilidad de 13.
- Un número es divisible por 13 si y si la suma alterna (alternativamente sumando y restando) de bloques de tres de derecha a izquierda es divisible por 13. Por ejemplo, 2911285 es divisible por 13 porque la suma alterna de bloques de tamaño 3 es 2 – 911 + 285 = -650 que es divisible por 13.
- Un número es divisible por 13 si y solo si el número obtenido al sumar el último dígito multiplicado por 4 al resto también es divisible por 13.
Por ejemplo, considere 2353. Aplicando la regla anterior, obtenemos 235 + 3*4 = 247. Nuevamente aplicamos regla y obtenga, 24 + 7*4 = 52. Dado que 52 es divisible por 13, el número dado es divisible por 13.
A continuación, se basa en la implementación un primer hecho anterior (Encontrar una suma alterna de bloques de tamaño 3)
C++
// CPP program to check
// whether a number is
// divisible by 13 or not.
#include <iostream>
using namespace std;
// Returns true if number
// is divisible by 13 else
// returns false
bool checkDivisibility(string num)
{
int length = num.size();
if (length == 1 && num[0] == '0')
return true;
// Append required 0s .
// at the beginning.
if (length % 3 == 1)
{
// Same as strcat(num, "00");
// in c.
num +="00";
length += 2;
}
else if (length % 3 == 2)
{
// Same as strcat(num, "0");
// in c.
num += "0";
length += 1;
}
// Alternatively add/subtract
// digits in group of three
// to result.
int sum = 0, p = 1;
for (int i = length - 1; i >= 0; i--)
{
// Store group of three
// numbers in group variable.
int group = 0;
group += num[i--] - '0';
group += (num[i--] - '0') * 10;
group += (num[i] - '0') * 100;
sum = sum + group * p;
// Generate alternate series
// of plus and minus
p *= (-1);
}
sum = abs(sum);
return (sum % 13 == 0);
}
// Driver code
int main()
{
string number = "83959092724";
if (checkDivisibility(number))
cout << number << " is divisible by 13.";
else
cout << number << " is not divisible by 13.";
return 0;
}
Java
// Java program to check
// whether a number is
// divisible by 13 or not.
class GFG
{
// Returns true if number
// is divisible by 13 else
// returns false
static boolean checkDivisibility(String num)
{
int length = num.length();
if (length == 1 &&
num.charAt(0) == '0')
return true;
// Append required 0s .
// at the beginning.
if (length % 3 == 1)
{
// Same as strcat(num, "00");
// in c.
num +="00";
length += 2;
}
else if (length % 3 == 2)
{
// Same as strcat(num, "0");
// in c.
num += "0";
length += 1;
}
// Alternatively add/subtract
// digits in group of three
// to result.
int sum = 0, p = 1;
for (int i = length - 1; i >= 0; i--)
{
// Store group of three
// numbers in group variable.
int group = 0;
group += num.charAt(i--) - '0';
group += (num.charAt(i--) - '0') * 10;
group += (num.charAt(i) - '0') * 100;
sum = sum + group * p;
// Generate alternate series
// of plus and minus
p *= (-1);
}
sum = Math.abs(sum);
return (sum % 13 == 0);
}
// Driver code
public static void main(String[] args)
{
String number = "83959092724";
if (checkDivisibility(number))
System.out.println(number +
" is divisible by 13.");
else
System.out.println(number +
" is not divisible by 13.");
}
}
// This code is contributed by mits
Python3
C#
// C# program to check
// whether a number is
// divisible by 13 or not.
using System;
class GFG {
// Returns true if number
// is divisible by 13 else
// returns false
static bool checkDivisibility(string num)
{
int length = num.Length;
if (length == 1 && num[0] == '0')
return true;
// Append required 0s .
// at the beginning.
if (length % 3 == 1)
{
// Same as strcat(num, "00");
// in c.
num +="00";
length += 2;
}
else if (length % 3 == 2)
{
// Same as strcat(num, "0");
// in c.
num += "0";
length += 1;
}
// Alternatively add/subtract
// digits in group of three
// to result.
int sum = 0, p = 1;
for (int i = length - 1; i >= 0; i--)
{
// Store group of three
// numbers in group variable.
int group = 0;
group += num[i--] - '0';
group += (num[i--] - '0') * 10;
group += (num[i] - '0') * 100;
sum = sum + group * p;
// Generate alternate series
// of plus and minus
p *= (-1);
}
sum = Math.Abs(sum);
return (sum % 13 == 0);
}
// Driver code
static void Main()
{
string number = "83959092724";
if (checkDivisibility(number))
Console.Write( number +
" is divisible by 13.");
else
Console.Write( number +
" is not divisible by 13.");
}
}
// This code is contributed by Sam007
PHP
<?php
// PHP program to check
// whether a number is
// divisible by 13 or not.
// Returns true if number
// is divisible by 13 else
// returns false
function checkDivisibility($num)
{
$length = strlen($num);
if ($length == 1 &&
$num[0] == '0')
return true;
// Append required 0s
// at the beginning.
if ($length % 3 == 1)
{
// Same as strcat(num, "00");
// in c.
$num += "00";
$length += 2;
}
else if ($length % 3 == 2)
{
// Same as strcat(num, "0");
// in c.
$num += "0";
$length += 1;
}
// Alternatively add/subtract
// digits in group of three
// to result.
$sum = 0; $p = 1;
for ($i = $length - 1; $i >= 0; $i--)
{
// Store group of three
// numbers in group variable.
$group = 0;
$group += $num[$i--] - '0';
$group += ($num[$i--] - '0') * 10;
$group += ($num[$i] - '0') * 100;
$sum = $sum + $group * $p;
// Generate alternate series
// of plus and minus
$p *= (-1);
}
$sum = abs($sum);
return ($sum % 13 == 0);
}
// Driver code
$number = "83959092724";
if (checkDivisibility($number))
echo($number . " is divisible by 13.");
else
echo($number . " is not divisible by 13.");
// This code is contributed by Ajit.
?>
Javascript
<script>
// Javascript program to check
// whether a number is
// divisible by 13 or not.
// Returns true if number
// is divisible by 13 else
// returns false
function checkDivisibility(num)
{
let length = num.length;
if (length == 1 &&
num[0] == '0')
return true;
// Append required 0s
// at the beginning.
if (length % 3 == 1)
{
// Same as strcat(num, "00");
// in c.
num += "00";
length += 2;
}
else if (length % 3 == 2)
{
// Same as strcat(num, "0");
// in c.
num += "0";
length += 1;
}
// Alternatively add/subtract
// digits in group of three
// to result.
let sum = 0; p = 1;
for (let i = length - 1; i >= 0; i--)
{
// Store group of three
// numbers in group variable.
group = 0;
group += num[i--] - '0';
group += (num[i--] - '0') * 10;
group += (num[i] - '0') * 100;
sum = sum + group * p;
// Generate alternate series
// of plus and minus
p *= (-1);
}
sum = Math.abs(sum);
return (sum % 13 == 0);
}
// Driver code
let number = "83959092724";
if (checkDivisibility(number))
document.write(number + " is divisible by 13.");
else
document.write(number + " is not divisible by 13.");
// This code is contributed by _saurabh_jaiswal.
</script>
Producción
83959092724 is divisible by 13.
Método: Comprobación de que el número dado es divisible por 13 o no utilizando el operador de división de módulo «%».
Python3
# Python code
# To check whether the given number is divisible by 13 or not
#input
n=83959092724
# the above input can also be given as n=input() -> taking input from user
# finding given number is divisible by 13 or not
if int(n)%13==0:
print("Yes")
else:
print("No")
# this code is contributed by gangarajula laxmi
Producción
Yes
Publicación traducida automáticamente
Artículo escrito por pawan_asipu y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA