Given multiple numbers and a number n, the task is to print the remainder after multiply all the number divide by n.

**Examples:**

Input : arr[] = {100, 10, 5, 25, 35, 14}, n = 11 Output : 9 100 x 10 x 5 x 25 x 35 x 14 = 61250000 % 11 = 9

**Naive approach:** First multiple all the number then take % by n then find the remainder, But in this approach, if the number is maximum of 2^64 then it give the wrong answer.

**Approach that avoids overflow :** First take a remainder or individual number like arr[i] % n. Then multiply the remainder with current result. After multiplication, again take remainder to avoid overflow. This works because of distributive properties of modular arithmetic. ( a * b) % c = ( ( a % c ) * ( b % c ) ) % c

`// C++ program to find` `// remainder when all` `// array elements are` `// multiplied.` `#include <iostream>` `using` `namespace` `std;` ` ` `// Find remainder of arr[0] * arr[1] *` `// .. * arr[n-1]` `int` `findremainder(` `int` `arr[], ` `int` `len, ` `int` `n)` `{` ` ` `int` `mul = 1;` ` ` ` ` `// find the individual remainder` ` ` `// and multiple with mul.` ` ` `for` `(` `int` `i = 0; i < len; i++)` ` ` `mul = (mul * (arr[i] % n)) % n;` ` ` ` ` `return` `mul % n;` `}` ` ` `// Driver code` `int` `main()` `{` ` ` `int` `arr[] = { 100, 10, 5, 25, 35, 14 };` ` ` `int` `len = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `int` `n = 11;` ` ` ` ` `// print the remainder of after` ` ` `// multiple all the numbers` ` ` `cout << findremainder(arr, len, n);` `}` |

**Output:**

9

Please refer complete article on Find remainder of array multiplication divided by n for more details!

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