Question

State whether the statement is True or False:

The HCF of two consecutive even numbers is $2$.

• A. True
• B. False

Answer 1

The correct option is A True

Finding the HCF of two consecutive even numbers:

Even Number: A number which is divisible by $2$ is called even number.

Lets take any two consecutive even numbers say $8$ and $10$,

On factorising $8$ and $10$, using prime factorisation method,we get,

The prime factorization of $8$ $=2\times 2\times 2$

The prime factorization of $10$ $=2\times 5$

The common prime factor is $2$

Therefore, the required $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ $=2$

Lets take any other two consecutive even numbers say $12$ and $14$,

On factorising $12$ and $14$, using prime factorisation method,we get,

The prime factorization of $12$ $=2\times 2\times 3$

The prime factorization of $14$ $=2\times 7$

The common prime factor is $2$

Therefore, the required $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ $=2$

Hence, the HCF of two consecutive even numbers is always $2$.

Hence, the given statement is True.