What is the product of the prime factorization of 36?

What is the product of the prime factorization of 36?

• A. 6
• B. 12
• C. 36
• D. 720

Answer: (C)

To determine the product of the prime factorization of 36, we first need to break down 36 into its prime factors. The number 36 can be expressed as 6 multiplied by 6, or 6². Further breaking down the number 6 reveals that it is the product of the primes 2 and 3 (since 6 = 2 × 3). Therefore, we have: 36 = 6 × 6 = (2 × 3) × (2 × 3) = 2² × 3². When we look at the product of the prime factorization, we are simply referring to the number itself from the original problem. So, calculating the prime factorization gives us the factors of 36 as 2² and 3², which when multiplied back together still gives us 36. Hence, the product of the prime factorization is 36, confirming that this response corresponds to the original number before any factorization took place.

To determine the product of the prime factorization of 36, we first need to break down 36 into its prime factors. The number 36 can be expressed as 6 multiplied by 6, or 6². Further breaking down the number 6 reveals that it is the product of the primes 2 and 3 (since 6 = 2 × 3). Therefore, we have:

36 = 6 × 6 = (2 × 3) × (2 × 3) = 2² × 3².

When we look at the product of the prime factorization, we are simply referring to the number itself from the original problem. So, calculating the prime factorization gives us the factors of 36 as 2² and 3², which when multiplied back together still gives us 36.

Hence, the product of the prime factorization is 36, confirming that this response corresponds to the original number before any factorization took place.