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 that has at least one positive divisor other than one and itself. Prime numbers have only 1 and themselves as divisors, and 1 is neither prime nor composite.

Step2: Analyze each factor pair

• For \(96\times1\): 1 is not composite, 96 is composite. So this pair fails.
• For \(48\times2\): 2 is a prime number (divisors 1 and 2), so this pair fails.
• For \(32\times3\): 3 is a prime number (divisors 1 and 3), so this pair fails.
• For \(12\times8\): 12 has divisors \(1, 2, 3, 4, 6, 12\) (composite), 8 has divisors \(1, 2, 4, 8\) (composite). Both are composite.

Answer:

\(12\times8\)