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How many five-digit numbers of the form \(\overline{32x5y}\) are divisible by 72?

 Oct 9, 2020
 #1
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to be divisible by 72, it has to be divisible by 8 and 9. To be divisible by 9, 3 + 2 + x + 5 + y has to be divisible by 9. So, 10+x+y is divisible by 9. Then, x5y has to be divisible by 8. Now, if you list it all out, you should get an answer.

 Oct 9, 2020
 #2
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Out of 100 integers of this form, I could find only one such number:  32256 mod 72 =0

 Oct 9, 2020
edited by Guest  Oct 9, 2020
 #3
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Thnaks, Guest!

 Oct 9, 2020

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