Question

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

Fractions
ANSWERED
asked 2021-02-21
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)

2021-02-22

Relatively Prime: Two integers are said to be relatively prime if there is no integer greater than one that divides them both.
Answer (a):Answer (a): The given numbers are 15 and 25.
Factorization of 15 is \(15=3 \times 5\) and the factorization of 25 is \(25=5 \times 5\)
Since 5 is the common factor in factorization of both the numbers, therefore they are not prime numbers.
Answer (b): The given numbers are 29 and 58.
Factorization of 29 is \(29=1 \times 29\) and the factorization of 58 is \(58=2 \times 29\)
Since 29 is the common factor in factorization of both the numbers, therefore they are not prime numbers.
Answer (c):
The given numbers are 40 and 63.
Factorization of 40 is \(40=1 \times 2 \times 2 \times 2 \times 5\)
and the factorization of 63 is \(63=1 \times 3 \times 3 \times 7\)
Since in the factorization of both the numbers, there is no common number than one, thus 4040 and 6363 are prime numbers.
Answer (d): The given numbers are 261 and 513.
Factorization of 261261 is \(261=3 \times 3 \times 29\) and the factorization of 513 is \(513=3 \times 3 \times 3 \times 19\)
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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