You are given an n-digit large number, you have to check whether it is divisible by 7.

A (r+1)-digit integer n whose digital form is **(ar ar-1 ar-2….a2 a1 a0)** is divisible by 7 if and only if the alternate series of numbers **(a2 a1 a0) – (a5 a4 a3) + (a8 a7 a6) – … **is divisible by 7.

The triplets of digits within parenthesis represent 3-digit number in digital form.

The given number n can be written as a sum of powers of 1000 as follows.

n= (a2 a1 a0) + (a5 a4 a3)*1000 + (a8 a7 a6)*(1000*1000) +….

As 1000 = (-1)(mod 7), 1000 as per congruence relation.

For a positive integer n, two numbers a and b are said to be congruent modulo n, if their difference

(a – b) is an integer multiple of n (that is, if there is an integer k such that a – b = kn). This congruence relation is typically considered when a and b are integers, and is denoted

Hence we can write:

n = { (a2a1a0) + (a5a4a3)* (-1) + (a8a7a6)* (-1)*(-1)+…..}(mod 7),

Thus n is divisible by 7 if and if only if the series is divisible by 7.

**Examples :**

Input : 8955795758 Output : Divisible by 7Explanation:We express the number in terms of triplets of digits as follows. (008)(955)(795)(758) Now, 758- 795 + 955 - 8 = 910, which is divisible by 7 Input : 100000000000 Output : Not Divisible by 7Explanation:We express the number in terms of triplets of digits as follows. (100)(000)(000)(000) Now, 000- 000 + 000 - 100 = -100, which is not divisible by 7

Note that the number of digits in n may not be multiple of 3 . In that case we pas zero(s) on the left side of the remaining digits(s) after taking out all the triplets (from right side of n) to form the last triplet.

A simple and efficient method is to take input in form of string (make its length in form of 3*m by adding 0 to left of number if required) and then you have to add the digits in blocks of three from right to left until it become a 3 digit number to form an alternate series and check whether the series is divisible by 7 or not.

Here the program implementation to check divisibility of 7 is done.

## C++

`// C++ code to check divisibility of a ` `// given large number by 7 ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `isdivisible7(` `char` `num[]) ` `{ ` ` ` `int` `n = ` `strlen` `(num), gSum; ` ` ` `if` `(n == 0 && num[0] == ` `'\n'` `) ` ` ` `return` `1; ` ` ` ` ` `// Append required 0s at the beginning. ` ` ` `if` `(n % 3 == 1) { ` ` ` `strcat` `(num, ` `"00"` `); ` ` ` `n += 2; ` ` ` `} ` ` ` `else` `if` `(n % 3 == 2) { ` ` ` `strcat` `(num, ` `"0"` `); ` ` ` `n++; ` ` ` `} ` ` ` ` ` `// add digits in group of three in gSum ` ` ` `int` `i, GSum = 0, p = 1; ` ` ` `for` `(i = n - 1; i >= 0; i--) { ` ` ` ` ` `// group saves 3-digit group ` ` ` `int` `group = 0; ` ` ` `group += num[i--] - ` `'0'` `; ` ` ` `group += (num[i--] - ` `'0'` `) * 10; ` ` ` `group += (num[i] - ` `'0'` `) * 100; ` ` ` ` ` `gSum = gSum + group * p; ` ` ` ` ` `// generate alternate series of plus ` ` ` `// and minus ` ` ` `p *= (-1); ` ` ` `} ` ` ` ` ` `return` `(gSum % 7 == 0); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `// Driver method ` ` ` `char` `num[] = ` `"8955795758"` `; ` ` ` `if` `(isdivisible7(num)) ` ` ` `cout << ` `"Divisible by 7"` `; ` ` ` `else` ` ` `cout << ` `"Not Divisible by 7"` `; ` ` ` `return` `0; ` `} ` ` ` `// This code is contributed ` `// by Akanksha Rai ` |

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## C

`// C code to check divisibility of a ` `// given large number by 7 ` `#include <stdio.h> ` `#include <string.h> ` `int` `isdivisible7(` `char` `num[]) ` `{ ` ` ` `int` `n = ` `strlen` `(num), gSum; ` ` ` `if` `(n == 0 && num[0] == ` `'\n'` `) ` ` ` `return` `1; ` ` ` ` ` `// Append required 0s at the beginning. ` ` ` `if` `(n % 3 == 1) { ` ` ` `strcat` `(num, ` `"00"` `); ` ` ` `n += 2; ` ` ` `} ` ` ` `else` `if` `(n % 3 == 2) { ` ` ` `strcat` `(num, ` `"0"` `); ` ` ` `n++; ` ` ` `} ` ` ` ` ` `// add digits in group of three in gSum ` ` ` `int` `i, GSum = 0, p = 1; ` ` ` `for` `(i = n - 1; i >= 0; i--) { ` ` ` ` ` `// group saves 3-digit group ` ` ` `int` `group = 0; ` ` ` `group += num[i--] - ` `'0'` `; ` ` ` `group += (num[i--] - ` `'0'` `) * 10; ` ` ` `group += (num[i] - ` `'0'` `) * 100; ` ` ` ` ` `gSum = gSum + group * p; ` ` ` ` ` `// generate alternate series of plus ` ` ` `// and minus ` ` ` `p *= (-1); ` ` ` `} ` ` ` ` ` `return` `(gSum % 7 == 0); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `// Driver method ` ` ` `char` `num[] = ` `"8955795758"` `; ` ` ` `if` `(isdivisible7(num)) ` ` ` `printf` `(` `"Divisible by 7"` `); ` ` ` `else` ` ` `printf` `(` `"Not Divisible by 7"` `); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java code to check divisibility of a given large number by 7 ` ` ` `class` `Test { ` ` ` `// Method to check divisibility ` ` ` `static` `boolean` `isDivisible7(String num) ` ` ` `{ ` ` ` `int` `n = num.length(); ` ` ` `if` `(n == ` `0` `&& num.charAt(` `0` `) == ` `'0'` `) ` ` ` `return` `true` `; ` ` ` ` ` `// Append required 0s at the beginning. ` ` ` `if` `(n % ` `3` `== ` `1` `) ` ` ` `num = ` `"00"` `+ num; ` ` ` `if` `(n % ` `3` `== ` `2` `) ` ` ` `num = ` `"0"` `+ num; ` ` ` `n = num.length(); ` ` ` ` ` `// add digits in group of three in gSum ` ` ` `int` `gSum = ` `0` `, p = ` `1` `; ` ` ` `for` `(` `int` `i = n - ` `1` `; i >= ` `0` `; i--) { ` ` ` ` ` `// group saves 3-digit group ` ` ` `int` `group = ` `0` `; ` ` ` `group += num.charAt(i--) - ` `'0'` `; ` ` ` `group += (num.charAt(i--) - ` `'0'` `) * ` `10` `; ` ` ` `group += (num.charAt(i) - ` `'0'` `) * ` `100` `; ` ` ` `gSum = gSum + group * p; ` ` ` `// generate alternate series of plus and minus ` ` ` `p = p * -` `1` `; ` ` ` `} ` ` ` ` ` `// calculate result till 3 digit sum ` ` ` `return` `(gSum % ` `7` `== ` `0` `); ` ` ` `} ` ` ` ` ` `// Driver method ` ` ` `public` `static` `void` `main(String args[]) ` ` ` `{ ` ` ` `String num = ` `"8955795758"` `; ` ` ` ` ` `System.out.println(isDivisible7(num) ? ` `"Divisible by 7"` `: ` `"Not Divisible by 7"` `); ` ` ` `} ` `} ` |

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## Python 3

`# Python 3 code to check divisibility ` `# of a given large number by 7 ` ` ` `def` `isdivisible7(num): ` ` ` `n ` `=` `len` `(num) ` ` ` `if` `(n ` `=` `=` `0` `and` `num[` `0` `] ` `=` `=` `'\n'` `): ` ` ` `return` `1` ` ` ` ` `# Append required 0s at the beginning. ` ` ` `if` `(n ` `%` `3` `=` `=` `1` `) : ` ` ` `num ` `=` `str` `(num) ` `+` `"00"` ` ` `n ` `+` `=` `2` ` ` ` ` `elif` `(n ` `%` `3` `=` `=` `2` `) : ` ` ` `num ` `=` `str` `(num) ` `+` `"0"` ` ` `n ` `+` `=` `1` ` ` ` ` `# add digits in group of three in gSum ` ` ` `GSum ` `=` `0` ` ` `p ` `=` `1` ` ` `for` `i ` `in` `range` `(n ` `-` `1` `, ` `-` `1` `, ` `-` `1` `) : ` ` ` ` ` `# group saves 3-digit group ` ` ` `group ` `=` `0` ` ` `group ` `+` `=` `ord` `(num[i]) ` `-` `ord` `(` `'0'` `) ` ` ` `i ` `-` `=` `1` ` ` `group ` `+` `=` `(` `ord` `(num[i]) ` `-` `ord` `(` `'0'` `)) ` `*` `10` ` ` `i ` `-` `=` `1` ` ` `group ` `+` `=` `(` `ord` `(num[i]) ` `-` `ord` `(` `'0'` `)) ` `*` `100` ` ` ` ` `GSum ` `=` `GSum ` `+` `group ` `*` `p ` ` ` ` ` `# generate alternate series of ` ` ` `# plus and minus ` ` ` `p ` `*` `=` `(` `-` `1` `) ` ` ` ` ` `return` `(GSum ` `%` `7` `=` `=` `0` `) ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `num ` `=` `"8955795758"` ` ` `if` `(isdivisible7(num)): ` ` ` `print` `(` `"Divisible by 7"` `) ` ` ` `else` `: ` ` ` `print` `(` `"Not Divisible by 7"` `) ` ` ` `# This code is contributed by ChitraNayal ` |

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## C#

`// C# code to check divisibility of a ` `// given large number by 7 ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `// Method to check divisibility ` ` ` `static` `bool` `isDivisible7(String num) ` ` ` `{ ` ` ` `int` `n = num.Length; ` ` ` `if` `(n == 0 && num[0] == ` `'0'` `) ` ` ` `return` `true` `; ` ` ` ` ` `// Append required 0s at the beginning. ` ` ` `if` `(n % 3 == 1) ` ` ` `num = ` `"00"` `+ num; ` ` ` ` ` `if` `(n % 3 == 2) ` ` ` `num = ` `"0"` `+ num; ` ` ` ` ` `n = num.Length; ` ` ` ` ` `// add digits in group of three in gSum ` ` ` `int` `gSum = 0, p = 1; ` ` ` `for` `(` `int` `i = n - 1; i >= 0; i--) { ` ` ` ` ` `// group saves 3-digit group ` ` ` `int` `group` `= 0; ` ` ` `group` `+= num[i--] - ` `'0'` `; ` ` ` `group` `+= (num[i--] - ` `'0'` `) * 10; ` ` ` `group` `+= (num[i] - ` `'0'` `) * 100; ` ` ` `gSum = gSum + ` `group` `* p; ` ` ` ` ` `// generate alternate series ` ` ` `// of plus and minus ` ` ` `p = p * -1; ` ` ` `} ` ` ` ` ` `// calculate result till 3 digit sum ` ` ` `return` `(gSum % 7 == 0); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `static` `public` `void` `Main() ` ` ` `{ ` ` ` `String num = ` `"8955795758"` `; ` ` ` ` ` `// Function calling ` ` ` `Console.WriteLine(isDivisible7(num) ? ` `"Divisible by 7"` `: ` `"Not Divisible by 7"` `); ` ` ` `} ` `} ` ` ` `// This code is contributed by Ajit. ` |

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## PHP

`<?php ` `// PHP code to check divisibility of ` `// a given large number by 7 ` ` ` `// Function to check divisibility ` `function` `isDivisible7(` `$num` `) ` `{ ` ` ` `$n` `= ` `strlen` `(` `$num` `) ; ` ` ` `if` `(` `$n` `== 0 && ` `$num` `[0] == ` `'0'` `) ` ` ` `return` `true; ` ` ` ` ` `// Append required 0s at the beginning. ` ` ` `if` `(` `$n` `% 3 == 1) ` ` ` `$num` `= ` `"00"` `. ` `$num` `; ` ` ` `if` `(` `$n` `% 3 == 2) ` ` ` `$num` `= ` `"0"` `. ` `$num` `; ` ` ` `$n` `= ` `strlen` `(` `$num` `); ` ` ` ` ` `// add digits in group of three in gSum ` ` ` `$gSum` `= 0 ; ` ` ` `$p` `= 1; ` ` ` `for` `(` `$i` `= ` `$n` `- 1; ` `$i` `>= 0; ` `$i` `--) ` ` ` `{ ` ` ` ` ` `// group saves 3-digit group ` ` ` `$group` `= 0; ` ` ` `$group` `+= ` `$num` `[` `$i` `--] - ` `'0'` `; ` ` ` `$group` `+= (` `$num` `[` `$i` `--] - ` `'0'` `) * 10; ` ` ` `$group` `+= (` `$num` `[` `$i` `] - ` `'0'` `) * 100; ` ` ` `$gSum` `= ` `$gSum` `+ ` `$group` `* ` `$p` `; ` ` ` ` ` `// generate alternate series ` ` ` `// of plus and minus ` ` ` `$p` `= ` `$p` `* -1; ` ` ` `} ` ` ` ` ` `// calculate result till 3 digit sum ` ` ` `return` `(` `$gSum` `% 7 == 0); ` `} ` ` ` `// Driver Code ` `$num` `= ` `"8955795758"` `; ` ` ` `echo` `(isDivisible7(` `$num` `) ? ` ` ` `"Divisible by 7"` `: ` ` ` `"Not Divisible by 7"` `); ` ` ` `// This code is contributed by Ryuga ` `?> ` |

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**Output:**

Divisible by 7

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