1. **State the problem:** Find how many positive factors of 72 are also multiples of 3. 2. **Prime factorization of 72:** $$72 = 2^3 \times 3^2$$ 3. **Total number of factors of 72:** The number of factors is given by multiplying one more than each exponent: $$(3+1)(2+1) = 4 \times 3 = 12$$ 4. **Factors of 72 that are multiples of 3:** A factor is a multiple of 3 if it contains at least one factor of 3, i.e., the exponent of 3 in the factor is at least 1. 5. **Counting factors with at least one 3:** - Possible exponents for 2: $0,1,2,3$ (4 options) - Possible exponents for 3: $1,2$ (2 options) Number of such factors = $4 \times 2 = 8$ 6. **Answer:** There are 8 positive factors of 72 that are multiples of 3. Therefore, the correct choice is (C) 8.