Question

What can be the maximum value of HCF of any two numbers a and b given that a<b?

• A. $\text{b}$
• B. $\text{a}\times \text{b}$
• C. $\text{a}$
• D. $\frac{\text{a}}{\text{b}}$

Answer 1

The correct option is C

$\text{a}$

All the factors of any number other than itself are lesser than the number.
The number itself is the greatest factor of any number.
For example, 1, 2, 3, and 6 are the factors of 6. The greatest factor is 6, the number itself.
$\therefore$ a is the greatest factor of a, and b is the greatest factor of b.
As a<b, b can't be a factor of a, but a can be a factor of b.
So, the maximum value of HCF for a and b can be 'a' which is possible when 'a' is a factor of b.