What is the prime factorization of 48?

What is the prime factorization of 48?

• A. 3 × 2 × 2 × 4
• B. 2 × 2 × 2 × 2 × 3
• C. 6 × 8
• D. 2 × 24

Answer: (B)

Prime factorization expresses a number as a product of primes only. To factor 48, divide by the smallest prime repeatedly: 48 ÷ 2 = 24, 24 ÷ 2 = 12, 12 ÷ 2 = 6, 6 ÷ 2 = 3, and 3 is prime. This yields 2 × 2 × 2 × 2 × 3, which is the same as 2^4 × 3. Other options mix in composite factors like 4, 6, or 8, which aren’t prime factors, so they don’t represent the prime factorization.

Prime factorization expresses a number as a product of primes only. To factor 48, divide by the smallest prime repeatedly: 48 ÷ 2 = 24, 24 ÷ 2 = 12, 12 ÷ 2 = 6, 6 ÷ 2 = 3, and 3 is prime. This yields 2 × 2 × 2 × 2 × 3, which is the same as 2^4 × 3. Other options mix in composite factors like 4, 6, or 8, which aren’t prime factors, so they don’t represent the prime factorization.