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How many natural-number factors does N have if N=2^4*3^8*5^2*7^2?

 Jun 30, 2021
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$(4+1)(8+1)(2+1)(2+1) = 5 \times 9 \times 3 \times 3 = 45 \times 9 = 450 - 45 = \boxed{405}$

 Jun 30, 2021

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