# Python Program for 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```

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

 `# Python3 program to ` `# find remainder when ` `# all array elements ` `# are multiplied. ` ` `  `# Find remainder of arr * arr ` `# * .. * arr[n-1] ` `def` `findremainder(arr, lens, n): ` `    ``mul ``=` `1` ` `  `    ``# find the individual ` `    ``# remainder and  ` `    ``# multiple with mul. ` `    ``for` `i ``in` `range``(lens):  ` `        ``mul ``=` `(mul ``*` `(arr[i] ``%` `n)) ``%` `n ` `     `  `    ``return` `mul ``%` `n ` ` `  `# Driven code ` `arr ``=` `[ ``100``, ``10``, ``5``, ``25``, ``35``, ``14` `] ` `lens ``=` `len``(arr) ` `n ``=` `11` ` `  `# print the remainder ` `# of after multiple ` `# all the numbers ` `print``( findremainder(arr, lens, n)) ` ` `  `# This code is contributed by "rishabh_jain". `

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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