Question

The product of two numbers is 6300 and their HCF is 15. How many pairs of such numbers are there?

• A. $32$
• B. $30$
• C. $28$
• D. $26$

Answer 1

The correct option is C $28$

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

It is given that the product of the two numbers is $6300$, therefore,

$xy=6300$

Also $15$ is their HCF, thus both numbers must be divisible by $15$.

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

$15a\times 15b=6300\Rightarrow 225ab=6300\Rightarrow ab=\frac{6300}{225}\Rightarrow ab=28$

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 $(60,105)$.

Hence, the number of possible pairs is $2$.