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How many perfect squares that are also its divisors are there  in 20! ? Thanks for help.

 Feb 26, 2020
 #1
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To get the number of perfect squares that are also divisors of 20! follow this procedure:


Take the exponent of those prime fators that have exponents, divide by 2 and add 1, and then multiply them all together:


[18/2 +1] x [8/2 +1] x [4/2 + 1] x [2/2 +1] =10 x 5 x 3 x 2 =300 prefect squares that are also divisors of 20!.

 Feb 26, 2020
 #2
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I neglected to include the factorization of 20! Sorry about that:

20! = 2,432,902,008,176,640,000 = 2^18 × 3^8 × 5^4 × 7^2 × 11 × 13 × 17 × 19

 Feb 26, 2020
edited by Guest  Feb 26, 2020
edited by Guest  Feb 26, 2020
edited by Guest  Feb 26, 2020

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