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.