The last digit in 7^300 is?

Question

a) 1
b) 9
c) 7
d) 3
e) 5

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Answer 1 · 2017-11-12T16:08:13

a) #1#

Let's look at powers of #7# modulo #10# ...

#7, 9, 3, 1, 7, 9, 3, 1,...#

So any power which is a multiple of #4# gives a last digit #1#.

#300 = 4 * 75#

So:

#7^300 -= 1# modulo #10#

Answer 2 · 2017-11-12T16:24:22

#1#

We have

#((7^1 = 7 -> 7),(7^2=49->9),(7^3=343->3),(7^4=2401->1),(cdots),(7^300= ?->1))#

because the remainder #r#

#7^n equiv r mod 10# is periodic with #n# and the period is #4#

but #300 equiv 0 mod 4# then #7^300 equiv 1 mod 10#