Question

Which of the following pair of numbers are $\text{relatively prime}$ :-

• A. 36 and 54
• B. 52 and 78
• C. 54 and 114
• D. 59 and 61

Answer 1

The correct option is D 59 and 61

The question must be which of the following are relatively primes?

$\left(a\right)$HCF$(36,54)$

Factors of $36=2\times 3\times 2\times 3$

Factors of $54=2\times 3\times 3\times 3$

Common factor$=2\times 3\times 3=18$

Hence HCF$=18$

$\therefore 36$ and $54$ are not relatively primes

$\left(b\right)$HCF$(52,78)$

Factors of $52=2\times 2\times 13$

Factors of $78=2\times 3\times 13$

Common factor$=2\times 13=26$

Hence HCF$=26$

$\therefore 52$ and $78$ are not relatively primes

$\left(c\right)$HCF$(54,114)$

Factors of $54=2\times 3\times 3\times 3$

Factors of $114=2\times 3\times 19$

Common factor$=2\times 3=6$

Hence HCF$=6$

$\therefore 54$ and $114$ are not relatively primes

$\left(d\right)$HCF$(59,61)$

Factors of $59=1\times 59$

Factors of $61=1\times 61$

Common factor$=1$

Hence HCF$=1$

$\therefore 59$ and $61$ are relatively primes

As $61-59=2$ they are also twin primes.