How many of the positive divisors of 600 are also multiples of 4 not including 600? Choose the correct choice from the following answers: A) 6 B) 8 C) 9 D) 11 E) 12
600 = 2^6 * 3 * 5 = (4) * 2 * 3 * 5^2   Besides (4), the exponents of 2, 3, and 5 are 1, 1, and 2.   There are (1+1)(1+1)(2+1) = 12 ways to make multiples of 4.   We must subtract 1 because one of these multiples is 600.   The answer is 11.
<result>D</result>
How many of the positive divisors of 600 are also multiples of 4 not including 600?