Question

The HCF of two numbers is $8$. The product of the two numbers is $1536$. How many pairs of such numbers satisfy the above conditions?

• A. One
• B. Two
• C. Four
• D. None of these

Answer 1

The correct option is B Two

Let the numbers be $8x;8y$, where $x,y$ are co-prime to each other.
Then $8x\times 8y=1536$
$=>xy=24$
Now, we need to find co-prime numbers whose product is $24$
$24=2^3\times 3$
Therefore co-prime pairs will be $(1,24);(8,3)$
Therefore, only two pairs of such numbers satisfy the given condition.