SOLUTION: If 713^10 is multiplied out completely, what is the units digit of the resulting number? (a) 0 (b) 1 (c) 3 (d) 7 (e) 9

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Question 339034: If 713^10 is multiplied out completely, what is the units digit of the resulting number?
(a) 0 (b) 1 (c) 3 (d) 7 (e) 9
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
When looking for a units digit of a large number, use mod 10
Since a number divisible by 10 ends in 0, the units digit will be the remainder when divided by 10.
Note that 713=23*31
So, we have %2823%5E2%29%5E5%2A%2831%5E2%29%5E5=713%5E10
Powers of 31 always end in 1 and 23^2 ends in 9
23^2==9(mod 10) and 31==1(mod 10)
9*1=9
The last digit is 9.
The idea with mod arithmetic like this is to break it up into smaller powers to work with.