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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)

 Sep 18, 2020
 #1
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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 $2^3*3^2$.

 Sep 18, 2020
 #5
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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
 #2
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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 !.

 Sep 18, 2020
 #3
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I get the following:

 

 Sep 18, 2020
 #4
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This is a problem from Middle School Contest Math at AoPS, and this problem is in this week's homework..

 Sep 19, 2020

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