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what is the largest perfect square that divides 479001600 or 12! ?

 Dec 24, 2019
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The prime factorization of 12! is 2^10(3^5)(5^2)(7)(11). Then, take the primes that are multiplied more than once, so 2^10, 3^4(leave the last 3 behind i will explain later), and 5^2. We want to make each exponent even because it must be a perfect square, which is why i didn't include the 5th 3. Therefore, the largest perfect square that divides 12! is 2^10 * 3^4 *5^2 = 2073600.

 Dec 24, 2019

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