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Find the number of distinct positive divisors of \((30)^4\) excluding 1 and \((30)^4\).

 Jan 1, 2019
 #1
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\(30=2^1 \cdot 3^1 \cdot 5^1\\ 30^4 = 2^4 \cdot 3^4 \cdot 5^4\\ \text{the number of divisors is equal to the product of 1 plus each exponent in the }\\ \text{prime factorization of a given number}\\ n = 5\cdot 5\cdot 5 = 125\)

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 Jan 1, 2019

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