Question

Two positive numbers have their HCF as $12$ and their product as $6336$. Choose the correct option for the number of pairs possible for the given numbers.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A

$2$

Explanation for the correct answer:

HCF of two numbers $=12$

Let $12xand12y$ be the numbers.

Now, according to the question,

$\begin{array}{rcl}12x\times 12y& =& 6336\\ 144xy& =& 6336\\ xy& =& 44\end{array}$

Now, $44$ can be expressed as $1\times 44,2\times 22,4\times 11$.

Since $xandy$ are co-prime, $(x,y)$ can be $(1,44)or(4,11)$.

Therefore two possible pairs exist.

Hence option A is the answer.