Question

the remainder of 2^100 when divided by 3

Answer 1

Hey there !

Solution:

Well the answer is simple.

There is a trick for all numbers which can be expressed in terms of powers of 2.

If the power of a number expressed in terms of 2 is even, then the remainder obtained when divided by 3 is 1. If the power of a number expressed in terms of 2 is odd, then the remainder is 2.

E.g. 2² = 4

It has an even power 2. So 4 when divided by 3 will give remainder 1.

E.g. 2³ = 8

It has an odd power 3. So 8 divided by 3 will give a remainder 2.

Since 2¹⁰⁰ is having an even power 100, the remainder obtained after dividing by 3 is 1.

Hope my answer helped !