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f(n) denotes the number of positive factors of a positive integer n. What is f(f(480))?

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f(n) denotes the number of positive factors of a positive integer n. What is f(f(480))?

by Max@Math Revolution » Tue Jun 16, 2020 2:01 am

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[GMAT math practice question]

f(n) denotes the number of positive factors of a positive integer n. What is f(f(480))?

A. 8
B. 14
C. 16
D. 20
E. 24
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Re: f(n) denotes the number of positive factors of a positive integer n. What is f(f(480))?

by Max@Math Revolution » Thu Jun 18, 2020 1:07 am
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Remember the formula for the number of factors of a positive integer N = p^a·q^b·r^c is (a + 1)(b + 1)(c + 1).
Since 480 has the prime factorization 480 = 32·3·5 = 2^5·3^1·5^1, 480 has (5 + 1)(1 + 1)(1 + 1) = 6·2·2 = 24 factors and we have f(480) = 24.
Since 24 has the prime factorization 24 = 8·3 = 2^3·3^1, 24 has (3 + 1)(1 + 1) = 4·2 = 8 factors and we have f(f(480)) = f(24) = 8.

Therefore, the answer is A.
Answer: A
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