Question

State whether the statement is True or False:

The HCF of two distinct prime numbers is $1$.

• A. True
• B. False

Answer 1

The correct option is A True

Finding the HCF of two distinct prime numbers:

Prime Numbers:The numbers which have only two factors $1$ and the number itself are called Prime Numbers.

For example: $2,3,5,7,11,13$ etc.

Lets take any two prime numbers say $2$ and $3$,

On factorising $2$ and $3$, using prime factorisation method,we get,

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

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

The common prime factor is $1$

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

Lets take any other two prime numbers say $5$ and $11$,

On factorising $5$ and $11$, using prime factorisation method,we get,

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

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, the HCF of two distinct prime numbers is always $1$.

Hence, the given statement is True.