Question

Which of the following pair is not co-prime?

• A. $5,30$
• B. $3,4$
• C. $7,11$
• D. $16,9$

Answer 1

The correct option is A

$5,30$

Explanation for correct option:

Option A : $5,30$

Co- Primes : If the highest common factor between two numbers is $1$, then the numbers are called Co-Primes.

On factorising $5$ and $30$, using prime factorisation method,we get,

The prime factorization of $5$ $=5\times 1$

The prime factorization of $30$ $=2\times 3\times 5$

The common prime factor is $5$

Therefore, the required $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ $=5$

Hence, $5,30$ are not co-primes.

Explanation for incorrect options:

Option B : $3,4$

On factorising $3$ and $4$, using prime factorisation method,we get,

The prime factorization of $4$ $=2\times 2\times 1$

The prime factorization of $3$ $=1\times 3$

The common prime factor is $1$

Therefore, the required $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ $=1$

Hence, $3,4$ are co-primes.

Option C : $7,11$

On factorising $7$ and $11$, using prime factorisation method,we get,

The prime factorization of $7$ $=1\times 7$

The prime factorization of $11$ $=1\times 11$

The common prime factor is $1$

Therefore, the required $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ $=1$

Hence, $7,11$ are co-primes.

Option D : $16,9$

On factorising $16$ and $9$, using prime factorisation method,we get,

The prime factorization of $16$ $=2\times 2\times 2\times 2\times 1$

The prime factorization of $9$ $=1\times 3\times 3$

The common prime factor is $1$

Therefore, the required $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ $=1$

Hence, $16,9$ are co-primes.

Hence, option A is the correct answer.