Question

Which numbers are not relatively prime?

1. $32,65$
2. $34,69$
   
3. $63,91$
   
4. $26,85$
   

Short answer

The correct option is C.

Step-by-step solution

Step -1 - Apply the concept of   Prime Factorization

In this, simply use the concept of Prime factorization of the numbers to get the greatest common factor of the given numbers.

Step -2 – Find the Factorization of the numbers

Since,

a. The factor of 32are:$32=2\times 2\times 2\times 2\times 2$

The factor of65 are:$65=5\times 13$

It has no common factor other than 1.

b. The factor of 34are:$34=2\times 17$

The factor of69 are:$69=3\times 23$

It has no common factor other than1 .

c. The factor of 63are:$63=3\times 3\times 7$

The factor of91 are:$91=7\times 13$

It has common factor which is 7other than 1.

d. The factor of26 are:$26=2\times 13$

The factor of 85are:$85=5\times 17$

It has no common factor other than 1.

Step -3 – Eliminating the options by giving reason

a.$32,65$ : It is not the correct option because it has only one factor .

b.$34,69$: It is not the correct option because it has only one factor .

c.$63,91$: It is the correct option because it has another factor other than .d. $26,85$: It is not the correct option because it has only one factor .