# 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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 Click here to see ALL problems on Numbers Word Problems 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) 9Answer by galactus(183)   (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 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.