Find the largest integer n for which 12^n evenly divides 20.

To add a bit, the reason 12^n can't be wholly divisable by 20 is because 20 = 2^2 * 5 and 12 = 2^2 * 3.

That means that 12^n will only have factors of 2 and 3 (assuming n is an integer).

Therefore, it will never be able to divide out the 5 in 20.

=^._.^=

Hello Guest!

\( n\in \mathbb Z\\ z=\dfrac{12^n}{20}\\\)

\(\large z\notin \mathbb Z\)

\(12 ^ n\) is in no case wholly divisible by 20.

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