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# Number Theory

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For how many positive integer values of n is 3^n a factor of $$15^{15}$$?

Apr 30, 2022

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We can write $$15^{15}$$ as $$3^{15} \times 5^{15}$$

Thus, n can be anything from 0 up to 15, making for $${16}$$ values

EDIT: Upon furthur inspection, I found that n can also be 18, making for $$\color{brown}\boxed{17}$$ values.

Apr 30, 2022
edited by BuilderBoi  Apr 30, 2022