Question

If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?

a. 8
b. 9
c. 12
d. 15
e. 27

Answer 1

d. 15

Explanation:

List the exponents of each of the prime factors. Here, they are 3, 1, 1.

Add 1 to each of these values and form the product of these sums:

(4)(2)(2) = 16

This is the number of divisors of the number. Since 1 is included in this count, 15 of the divisors are greater than 1.