Question

A prime factorization is the product of prime numbers that multiply to give the original number. What is the prime factorization of 48?

a) 2^4 * 3
b) 2 * 2 * 2 * 2 * 3
c) 2^2 * 2^2 * 3
d) 2 * 3 * 4 * 4

Answer 1

The prime factorization of 48 is found by dividing by the smallest prime number, 2, and continuing until only prime numbers are left. It results in 2 x 2 x 2 x 2 x 3, or using exponents, expressed as 2^4 x 3, which matches option (a).

Step-by-step explanation:

The prime factorization of a number is the expression of the number as a product of prime numbers. When factorizing the number 48, we can start by dividing it by the smallest prime number, which is 2. After the first division, we get 24. We continue dividing by 2 until we can no longer divide evenly by 2. The steps are as follows:

1. 48 ÷ 2 = 24
2. 24 ÷ 2 = 12
3. 12 ÷ 2 = 6
4. 6 ÷ 2 = 3
5. Since 3 is a prime number, we have completed the factorization.

Therefore, the prime factorization of 48 can be written as 2 x 2 x 2 x 2 x 3. Using exponents to express this more concisely, we would write it as 2^4 × 3. So, the correct answer from the given options is (a) 24 × 3.