What is the prime factorization of 60?

What is the prime factorization of 60?

• A. 2^3 × 3 × 5
• B. 2 × 3 × 5
• C. 2^2 × 5
• D. 2^2 × 3 × 5

Answer: (D)

Prime factorization breaks a number down into prime numbers that multiply to the original number. For 60, you can start by dividing by 2, since 60 is even: 60 = 2 × 30. Then factor 30, which is also even, giving 30 = 2 × 15. Now you have 15, which isn’t divisible by 2, so factor 15 as 3 × 5. All the factors are prime, so combine them: 60 = 2^2 × 3 × 5. This matches the product 4 × 3 × 5 = 60. If you tried 2^3 × 3 × 5, that would be 8 × 3 × 5 = 120, which is too large. If you used only one 2, you’d have 2 × 3 × 5 = 30, which is too small. If you used 2^2 × 5, you’d get 4 × 5 = 20, missing the 3.

Prime factorization breaks a number down into prime numbers that multiply to the original number. For 60, you can start by dividing by 2, since 60 is even: 60 = 2 × 30. Then factor 30, which is also even, giving 30 = 2 × 15. Now you have 15, which isn’t divisible by 2, so factor 15 as 3 × 5. All the factors are prime, so combine them: 60 = 2^2 × 3 × 5.

This matches the product 4 × 3 × 5 = 60. If you tried 2^3 × 3 × 5, that would be 8 × 3 × 5 = 120, which is too large. If you used only one 2, you’d have 2 × 3 × 5 = 30, which is too small. If you used 2^2 × 5, you’d get 4 × 5 = 20, missing the 3.