Question

which pairs of numbers are relatively prime? select all that apply.

12 and 25
12 and 27
14 and 21
15 and 32

Explanation:

Identify the definition of relatively prime

Two numbers are relatively prime if their greatest common factor (GCF) is \(1\).

Analyze each pair of numbers

• 12 and 25:

Factors of \(12\): \(1, 2, 3, 4, 6, 12\)
Factors of \(25\): \(1, 5, 25\)
\(\text{GCF}(12, 25) = 1\) (Relatively prime)

• 12 and 27:

Factors of \(12\): \(1, 2, 3, 4, 6, 12\)
Factors of \(27\): \(1, 3, 9, 27\)
\(\text{GCF}(12, 27) = 3
eq 1\) (Not relatively prime)

• 14 and 21:

Factors of \(14\): \(1, 2, 7, 14\)
Factors of \(21\): \(1, 3, 7, 21\)
\(\text{GCF}(14, 21) = 7
eq 1\) (Not relatively prime)

• 15 and 32:

Factors of \(15\): \(1, 3, 5, 15\)
Factors of \(32\): \(1, 2, 4, 8, 16, 32\)
\(\text{GCF}(15, 32) = 1\) (Relatively prime)

Select the correct options

The relatively prime pairs are \(12 \text{ and } 25\) and \(15 \text{ and } 32\).

Answer:

• 12 and 25 (Correct answer)
• 12 and 27
• 14 and 21
• 15 and 32 (Correct answer)