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

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.
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.
Factorization of 40 is $$40=1 \times 2 \times 2 \times 2 \times 5$$
and the factorization of 63 is $$63=1 \times 3 \times 3 \times 7$$
Factorization of 261261 is $$261=3 \times 3 \times 29$$ and the factorization of 513 is $$513=3 \times 3 \times 3 \times 19$$