State true or False:

The H.C.F of the given numbers cannot be lesser than the numbers themselves​.

The Statement is False.

Let us take any two numbers 56 and 84.

We have, 56 = 2 × 2 × 2 × 7 and,

84 = 2 × 2 × 3 × 7.

Now, HCF of 56 and 84 will be the product of common prime factors with the lowest exponential power, that is, 7 and 2².

So, HCF of 56 and 84 = 7 × 2 × 2 = 28.

Here, 28 is not greater than 56 and 84.

The H.C.F of the given numbers cannot be greater than the numbers themselves​.