Question

relating factors and multiples ii - item 2221
each answer choice is a factor pair of 96.
which factor pair contains only composite numbers?
96 × 1
48 × 2
32 × 3
12 × 8

Explanation:

Step1: Recall composite number definition

A composite number is a positive integer greater than 1 that has more than two positive divisors (i.e., not prime and not 1).

Step2: Analyze \(96\times1\)

• \(96\) is composite (divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96).
• \(1\) is neither prime nor composite. So this pair is invalid.

Step3: Analyze \(48\times2\)

• \(48\) is composite (divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48).
• \(2\) is prime (only divisors 1 and 2). So this pair is invalid.

Step4: Analyze \(32\times3\)

• \(32\) is composite (divisors: 1, 2, 4, 8, 16, 32).
• \(3\) is prime (only divisors 1 and 3). So this pair is invalid.

Step5: Analyze \(12\times8\)

• \(12\) is composite (divisors: 1, 2, 3, 4, 6, 12).
• \(8\) is composite (divisors: 1, 2, 4, 8). Both are composite.

Answer:

\(12\times8\)