Question

Choose the correct prime factorization of 96.

A. 2^5
B. 3^4 + 5^3
C. 3^4 + 3^5
D. 3^4 + 3^5 + 5^3

Answer 1

The prime factorization of 96 is achieved by dividing by 2 repeatedly until we are left with 3, a prime number. This results in the factorization 2^5 x 3, making the correct answer A. 2^5.

Step-by-step explanation:

To find the correct prime factorization of 96, we can use the process of repeatedly dividing by the smallest possible prime number until the result is 1. The steps are as follows:

• Divide 96 by 2 (the smallest prime number), which gives us 48.
• Continuing with 48, we divide by 2 again to get 24.
• We divide 24 by 2 to get 12.
• Dividing 12 by 2 gives us 6.
• Finally, dividing 6 by 2 gives us 3, which is a prime number and cannot be divided further.

Therefore, the prime factorization of 96 is 25 × 3, since we divided by 2 five times and ended with a 3. So, the correct answer is A. 25, because the other options do not accurately represent the prime factorization of 96.