Question

The sum of two numbers is $204$ and their HCF is $17$. Find the number of all the possible pairs of such numbers.

• A. $119$
• B. $120$
• C. $121$
• D. $117$

Answer 1

Answer: (A)

$119$

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

It is given that the sum of the two numbers is $204$, therefore,

$x+y=204$

Also $17$ is their HCF, thus both numbers must be divisible by $17$.

So, let $x=17a$ and $y=17b$, then

$17a+17b=204\Rightarrow 17(a+b)=204\Rightarrow a+b=\frac{204}{17}\Rightarrow a+b=12$

Therefore, required possible pair of values of $x$ and $y$ which are prime to each other are $(1,11)$ and $(5,7)$.

Thus, the required numbers are $(17,187)$ and $(85,119)$.

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