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Wed Oct 14, 2020 12:23 pm

E-GMAT

If n is the product of all odd prime numbers less than 16, how many factors does n have?

A. 5
B. 6
C. 16
D. 32
E. 64

OA D

Solution:

Recall that to determine the number of positive factors that a number n has, we first prime factorize n and then add 1 to each prime’s exponent. We then calculate the product of those “adjusted” exponents.

First, we prime factorize n:

n = 3^1 x 5^1 x 7^1 x 11^1 x 13^1

We add 1 to each exponent and then find the product of the adjusted exponents. Therefore, n has (1 + 1) x (1 + 1) x (1 + 1) x (1 + 1) x (1 + 1) = 2^5 = 32 factors.

Answer: D