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# help

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

Jan 1, 2019

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