Number Theory

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!.

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