What is the prime factorization of 60?

• A. 2^2 * 3 * 5
• B. 2^3 * 3 * 5
• C. 2 * 3 * 5
• D. 2^2 * 5 * 7

Answer: (A)

Prime factorization means writing a number as a product of prime numbers. To factor 60, divide by the smallest prime, 2: 60 = 2 × 30. Divide by 2 again: 30 = 2 × 15. Then 15 is divisible by 3: 15 = 3 × 5. Since 3 and 5 are primes, we’ve finished. The primes we used are two 2s, one 3, and one 5, so 60 = 2^2 × 3 × 5.

If you check the other expressions: 2^3 × 3 × 5 equals 120, not 60; 2 × 3 × 5 equals 30, not 60; and 2^2 × 5 × 7 equals 140, which isn’t 60. So the correct prime factorization is 2^2 × 3 × 5.