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How many perfect cubes are also factors, or divisors, of 25! (factorial)?. Thank you for any help.

 Nov 6, 2019
 #1
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25! =1.5511210043330985984e+25 = 2^22 * 3^10 * 5^6 * 7^3 * 11^2 * 13 * 17 * 19 * 23


Take the exponent, if it is 3 or greater, of any prime factor and divide it by 3 plus 1. Then multiply them all together.


So, (22/3 +1) * (10/3 + 1) * (6/3 + 1) * (3/3 + 1) =
          8          *      4          *      3       *      2        =192 perfect cubes that are also divisors of 25!.

 Nov 6, 2019
 #2
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Nice job guest! I learned from this one :)

CalculatorUser  Nov 6, 2019

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