Question

find remainder (7 ^ 688) ÷ 400​

Answer 1

Therefore the remainder of the number 7⁶⁸⁸ / 400 is '1'.

Given:

The number = 7⁶⁸⁸ / 400

To Find:

The remainder of 7⁶⁸⁸ / 400

Solution:

This numerical can be easily solved by the following approach.

Let x = 7⁶⁸⁸ / 400

⇒ 7⁴/400= 2401/400 ⇒ Remainder =1. This pattern continues for every power which is a multiple of '4' ( 4,8,12...)

Now 688 can be written as 4 × 172. So 688 is a multiple of '4'.

⇒ 7⁶⁸⁸ can be written as  ( 7⁴ )¹⁷². So if  7⁶⁸⁸ is divided by 400 we will get the remainder as '1'.

Therefore the remainder of the number 7⁶⁸⁸ / 400 is '1'.

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