How many five-digit numbers of the form 32x5y are divisible by 72?

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814

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+85

How many five-digit numbers of the form 32x5y are divisible by 72?

Thanks for helping! Also- please, please, PLEASE explain your answers; or else just don't; it's the same as not answering because I didn't learn anything)

PocketThePenguin Sep 18, 2020

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5⁺⁰ Answers

+1

The prime factorization of 72 is $2^3*3^2$, and so in order of 32x5y to be divisable by 72, it's prime factorization must include $2^3*3^2$.

Guest Sep 18, 2020

+1

A few AoPs questions sent from him/her were sent a few weeks ago when it was that weeks homework as well lmao

Guest Sep 25, 2020

+1

I can see only one such number that is divisible by 72 =32256. There isn't really anything to explain! You simply try every combination of 2 and 3 until you find it !.

Guest Sep 18, 2020

+33661

+5

I get the following:

Alan Sep 18, 2020

-1

This is a problem from Middle School Contest Math at AoPS, and this problem is in this week's homework..

Guest Sep 19, 2020

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