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

Ramsey 2021-02-09 Answered
Which pair of numbers is relatively prime?
a. 15 and 25
b. 29 and 58
c. 40 and 63
d. 261 and 513
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Expert Answer

StrycharzT
Answered 2021-02-10 Author has 102 answers

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 2

61=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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