Question

Heather and Gene each wrote the prime factorization of 96. Analyze their work and explain any errors.
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Part 1
Choose the correct answer below.
A.
Heather used a factor tree to find the correct prime factorization of 96. Gene listed factors of 96​, but some factors listed are not prime numbers.
B.
Gene listed the factors until all factors were prime numbers to find the correct prime factorization of 96. Heather used a factor​ tree, but not all branches end with prime numbers.
C.
Neither Heather nor Gene found the correct prime factorization of 96. Heather used a factor​ tree, but not all branches end with prime numbers. Gene listed factors of 96​, but some factors listed are not prime numbers.
D.
Both Heather and Gene found the correct prime factorization of 96. Heather used a factor tree. Gene listed the factors until all factors were prime numbers.
Choose the correct answer below.

Answer 1

Answer: A.

Explanation: Heather’s factor tree (when fully broken down) gives only prime factors: 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2^5 · 3, so her prime factorization is correct. Gene only listed factor pairs of 96 (for example 2·48, 3·32, 4·24, etc.); several of those factors (4, 24, 48, …) are not prime, so his work is not a prime factorization. To finish Gene’s work he would need to continue factoring the composite factors until all factors are prime.