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

[M7MBA]

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

Answer: D

Source: e-GMAT

[Scott@TargetTestPrep]

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

Answer: D

Solution:

We see that n = 3^1 x 5^1 x 7^1 x 11^1 x 13^1, and thus n has (1 + 1) x (1 + 1) x (1 + 1) x (1 + 1) x (1 + 1) = 2^5 = 32 factors.

Answer: D