# The sum of two positive integers 'a' and 'b' is 528 and their HCF is 33. Which of the following cannot be the value of (a - b)? (A) 396 (B) 264 (C) 6 (D) 33

Aug 9, 2018

The right option is (C) $6$.

#### Explanation:

The HCF of $a , b \in \mathbb{N}$ is $33$.

$\therefore a = 33 x \mathmr{and} b = 33 y$ for some $x , y \in \mathbb{N}$.

Utilising this in the Given that $a + b = 528$, we have,

$33 x + 33 y = 528$.

Now, $a - b = 33 x - 33 y = 33 \left(x - y\right) = 33 m , \text{ say, } m \in \mathbb{N}$.

This shows that $\left(a - b\right)$ must be a multiple of $33$.

Therefore, the right option is (C) $6$.