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

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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StrycharzT

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.