Question

2^31 is divisible with 5 what is the remainder?

Answer 1

Answer:

3

Step-by-step explanation:

When 2^x is divided by 5 then the remainder always be one of 2,4,3 & 1 in that order.

The digits of the remainder repeat after every 4 digits (2, 4, 3, 1, 2, 4, 3, 1...)

This property is called cyclicity.

To find out the remainder when 2^31 is divided by 5, we divide the power by the cyclicity of its base and obtain the remainder.

>> 31/4  (remainder = 3)

Now we use this remainder as the power and apply it to the same base.

>> 2^3 = 8

Now divide this by 5.

>> 8/5 (The remainder is (3))

Due to the nature of this method, 2^31 /5 will give us the same remainder when 2^3 is divided by 5.

Answer = 3