When a number is divided by 64, the remainder is 31. What will be the remainder when the same number is divided by 32?

Given:

A number leaves a remainder of 31 when divided by 64. We need to find the remainder when the same number is divided by 32.

Formula Used:

Let the number be represented as n. When n is divided by 64, the remainder is 31. This can be expressed as:

n = 64q + 31

where q is the quotient when n is divided by 64.

Calculations:

We are now interested in finding the remainder when n is divided by 32. Substituting n = 64q + 31 into this division:

n = 64q + 31 = 32(2q) + 31

This shows that when n is divided by 32, the remainder is the same as the remainder when 31 is divided by 32.

Since 31 is less than 32, the remainder when 31 is divided by 32 is simply 31.

The remainder when the number is divided by 32 is 31.