"Which pair of numbers is relatively prime?

A. 7 and 21
B. 4 and 15
C. 6 and 9
D. 9 and 27"

Question

"Which pair of numbers is relatively prime?

A. 7 and 21
B. 4 and 15
C. 6 and 9
D. 9 and 27"

CramX · Accepted Answer

Step 1: : Recall the definition of relatively prime numbers.. Two numbers are said to be relatively prime if their greatest common divisor (GCD) is 1. Step 2: : Determine the GCD for each pair of numbers.. (A) 7 and 21: 	ext{GCD}(21, 7) = \boxed{7} Since the GCD is not 1, these numbers are not relatively prime. (B) 4 and 15: 	ext{GCD}(15, 4) = 	ext{GCD}(4, 	ext{remainder of } 15 \div 4) = 	ext{GCD}(4, 3) = 	ext{GCD}(3, 	ext{remainder of } 4 \div 3) = 	ext{GCD}(3, 1) = \boxed{1} Since the GCD is 1, these numbers are relatively prime. (C) 6 and 9: 	ext{GCD}(9, 6) = 	ext{GCD}(6, 	ext{remainder of } 9 \div 6) = 	ext{GCD}(6, 3) = 	ext{GCD}(3, 	ext{remainder of } 6 \div 3) = 	ext{GCD}(3, 0) = \boxed{3} Since the GCD is not 1, these numbers are not relatively prime. (D) 9 and 27: 	ext{GCD}(27, 9) = 	ext{GCD}(9, 	ext{remainder of } 27 \div 9) = 	ext{GCD}(9, 0) = \boxed{9} Since the GCD is not 1, these numbers are not relatively prime. Final Answer: The pair of numbers that are relatively prime is (B) 4 and 15.

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Step 1:
: Recall the definition of relatively prime numbers.

Step 2:
: Determine the GCD for each pair of numbers.

Final Answer

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