Question

The product of two numbers is $6300$ and their $H.C.F.$ is $15.$ How many pairs of such numbers are there$?$

• A. $2$
• B. $6$
• C. $10$
• D. $3$

Answer 1

The correct option is A

$2$

It is given that product of two numbers is $6300$

Let $x$ and $y$ be the numbers.

Product $=xy$

$xy=6300$

$H.C.F=15$

So let $x=15a$ and $y=15b$

$225ab=6300$

$ab=\frac{6300}{225}$

$ab=28$

Therefore, required possible pair of values of $x$ and $y$ which are prime to each other are $(1,28)$ and $(4,7).$

Thus, the required numbers are $(15,420)$and $(60,105).$

Number of possible pairs $=2$

Hence, option $\left(A\right)$ is the correct answer.