# Java Program to Find remainder of array multiplication divided by n

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```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 gives 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.

 `// Java program to find ` `// remainder when all ` `// array elements are ` `// multiplied. ` `import` `java.util.*; ` `import` `java.lang.*; ` ` `  `public` `class` `GfG { ` ` `  `    ``// Find remainder of arr[0] * arr[1] * ` `    ``// .. * arr[n-1] ` `    ``public` `static` `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 function ` `    ``public` `static` `void` `main(String argc[]) ` `    ``{ ` `        ``int``[] arr = ``new` `int``[] { ``100``, ``10``, ``5``, ` `                                ``25``, ``35``, ``14` `}; ` `        ``int` `len = ``6``; ` `        ``int` `n = ``11``; ` ` `  `        ``// print the remainder of after ` `        ``// multiple all the numbers ` `        ``System.out.println(findremainder(arr, len, n)); ` `    ``} ` `} ` ` `  `/* This code is contributed by Sagar Shukla */`

Output:

```9
```

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

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Improved By : Akanksha_Rai

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