Questions: 16. Which pair of numbers below is relatively prime? Circle your answer. a. 15 and 21 b. 24 and 36 c. 45 and 32 d. 26 and 39

16. Which pair of numbers below is relatively prime? Circle your answer. a. 15 and 21 b. 24 and 36 c. 45 and 32 d. 26 and 39
Transcript text: 16. Which pair of numbers below is relatively prime? Circle your answer. a. 15 and 21 b. 24 and 36 c. 45 and 32 d. 26 and 39
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Solution

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Solution Steps

Step 1: Understanding Relatively Prime Numbers

Two numbers are relatively prime if their greatest common divisor (GCD) is 1. This means they have no common positive integer factors other than 1.

Step 2: Calculate GCD for Each Pair

  • Pair a: 15 and 21

    • Factors of 15: 1, 3, 5, 15
    • Factors of 21: 1, 3, 7, 21
    • Common factors: 1, 3
    • GCD: 3

  • Pair b: 24 and 36

    • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
    • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
    • Common factors: 1, 2, 3, 4, 6, 12
    • GCD: 12

  • Pair c: 45 and 32

    • Factors of 45: 1, 3, 5, 9, 15, 45
    • Factors of 32: 1, 2, 4, 8, 16, 32
    • Common factor: 1
    • GCD: 1

  • Pair d: 26 and 39

    • Factors of 26: 1, 2, 13, 26
    • Factors of 39: 1, 3, 13, 39
    • Common factors: 1, 13
    • GCD: 13
Step 3: Identify the Relatively Prime Pair

From the calculations above, the pair with a GCD of 1 is 45 and 32.

Final Answer

The pair of numbers that are relatively prime is \(\boxed{\text{c. 45 and 32}}\).

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