Which pair of numbers is relatively prime? a. 15 and 25 b. 29 and 58 c. 40 and 63 d. 261 and 513

Question
Algebra foundations
asked 2021-02-09
Which pair of numbers is relatively prime?
a. 15 and 25
b. 29 and 58
c. 40 and 63
d. 261 and 513

Answers (1)

2021-02-10
Relatively Prime: Two integers are said to be relatively prime if there is no integer greater than one that divides them both.
(a): Factorization of 15 is 15 = 3 * 5 and the factorization of 25 is
25 = 5 × 5
Since 5 is the common factor in factorization of both the numbers, therefore they are not prime numbers.
(b): Factorization of 29 is 29 = 1 × 29 and the factorization of 58 is 58 = 2 × 29
Since 29 is the common factor in factorization of both the numbers, therefore they are not prime numbers.
(c): Factorization of 40 is 40 = 1 × 2 × 2 × 2 × 5
and the factorization of 63 is 63 = 1 × 3 × 3 × 7
Since in the factorization of both the numbers, there is no common number than one, thus 40 and 63 are prime numbers.
(d): Factorization of 261 is 261 = 3 × 3 × 29
and the factorization of 513 is 513 = 3 × 3 × 3 × 19 Since 3 is the common factor in factorization of both the numbers, therefore they are not prime numbers. Thus, the pair 261 and 513 are not relatively prime.
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