How many of the positive divisors of 360 are also multiples of 4 not including 360?
Choose the correct option.
A) 8 B) 11 C) 12 D) 15 E) 16
360 = 2^5 * 3 * 5 = (4) * 2 * 3^2 * 5   Besides (4), the exponents of 2, 3, and 5 are 1, 2, and 1.   There are (1+1)(2+1)(1+1) = 12 ways to make multiples of 4.   We must subtract 1 because one of these multiples is 360.   The answer is 11.
<result>B</result>
How many of the positive divisors of 360 are also multiples of 4 not including 360?