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

Question

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?

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Answer 1 · 2018-05-13T11:46:37

The last digit will be #2#

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.