Question

Which of the following is coprime?

• A. $13and14$
• B. $8and20$
• C. $31and59$
• D. $34and85$

Answer 1

Answer: (A), (C)

$31and59$

Determine the co-prime.

Co-prime numbers or relatively prime numbers are those numbers that have their HCF (Highest Common Factor) as $1$.

Calculate the value for the given points:

For point A)

$$\begin{gathered} \Rightarrow 14=13\times 1+1 \\ \Rightarrow 13=1\times 13+0 \end{gathered}$$

HCF is $1$.so it is co-prime.

For point B)

$$\begin{gathered} \Rightarrow 20=8\times 2+4 \\ \Rightarrow 8=4\times 2+0 \end{gathered}$$

HCF is $4$ so, it is not co-prime.

For point C)

$$\begin{gathered} \Rightarrow 59=31\times 1+28 \\ \Rightarrow 31=28\times 1+3 \\ \Rightarrow 28=3\times 7+1 \\ \Rightarrow 3=1\times 3+0 \end{gathered}$$

HCF is $1$ so,it is co-prime.

For point D)

$$\begin{gathered} 85=34\times 2+17 \\ 34=17\times 2+0 \end{gathered}$$

HCF is $17$ so it is not a co-prime.

Hence, the correct option is “Option A and Option C”.