Python Program for Find Remainder of Array Multiplication Divided by N

Given an array of numbers and an integer n, the task is to find the remainder when all numbers in the array are multiplied and divided by n.

Examples:

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

Let’s explore different methods to find the remainder one by one:

Using Modular Multiplication

Here, modular arithmetic is used to avoid overflow. Instead of multiplying all numbers at once, we take the remainder of each number with n during multiplication:

(a * b) % n = ((a % n) * (b % n)) % n

arr = [100, 10, 5, 25, 35, 14]
n = 11
mul = 1
for num in arr:
    mul = (mul * (num % n)) % n

print(mul)

9

Explanation:

• Start with mul = 1.
• Multiply first element 100 -> (1 * 100) % 11 = 1
• Multiply next 10 -> (1 * 10) % 11 = 10
• Continue for all elements -> final remainder 9.

Using functools.reduce

The reduce function from functools can iterate through the array, multiplying elements and taking modulo n at each step.

from functools import reduce
arr1 = [100, 10, 5, 25, 35, 14]
n1 = 11
rem1 = reduce(lambda x, y: (x * y) % n1, arr1)
print(rem1)

9

Naive Multiplication

This method multiplies all numbers first and then applies modulo n. It’s simple but can overflow if the numbers are large.

arr = [100, 10, 5, 25, 35, 14]
n = 11
prd = 1
for num in arr:
    prd *= num

print(prd % n)

9

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