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Bunuel
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Bunuel
What is the remainder when the number 14^2*15^8 is divided by 5?

A. 0
B. 1
C. 2
D. 4
E. 5

No matter what 14^2 is, 15^8 will give a 5 at the end, which will be divisible by 5.
So ans is A.
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harucci
This post is not written properly. Since parentheses are needed to illustrate the exact operations.
In the current way written (14^2*15^8) it means: 14^{2*15^{8}}

The OptimusPrepJanielle gave a solution for (14^2)*(15^8) and this is perfectly divided by 5, since 15 is divided perfectly by 3, hence the quotient is an integer and the remainder 0. Which requires 0 operations.

The author should clarify what the right notation is.
Hi harucci,

Thanks a lot for pointing this out, I have included the parenthesis in my original post.
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We need to find the remainder when the number 14^2 * 15^8 is divided by 5

Theory
: Remainder of a number by 5 = Remainder of the units digit of the number by 5

Units digit of 14^2 * 15^8 = 6 * 5 (as units digit of any positive integer power of 5 is 5)
= Units digit of 30 = 0

=> Remainder of 14^2 * 15^8 by 5 = Remainder of 0 by 5 = 0

So, Answer will be A
Hope it helps!

MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

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