What is the last digit of this number? 2222^3333

Q. Find the last digit of 2222^3333
I know that this is the same thing as finding the remainder when divided by 10 (mod 10). But how do we go about it?

1 Answer
May 13, 2018

The last digit will be 2

Explanation:

The powers of 2 are 2,4,8,16,32,64,128,256 ....

The last digits form the pattern, 2,4,8,6 with the same order of these four digits repeating again and again.

The powers of any number where the last digit is 2 will have the same pattern for the last digit.
After a group of 4 the pattern starts again.

We need to find where 3333 falls in the pattern.

3333div 4 = 833 1/4

This means that the pattern has repeated 833 times followed by one number of the new pattern, which would be 2.

2222^3332 would end on a 6

2222^3333 will have 2 as the last digit.