Number System

HCF & LCM

Medium

The product of two positive integers $x$ and $y$ is 6760 and their HCF is 13. How many such pairs $(x, y)$ can be formed?

✅ Correct Option: 1

The HCF is 13, so write

$x=13a$ and $y=13b$ , where $a$ and $b$ share no common factor.

$xy=6760$

$\Rightarrow 169ab=6760$

$\Rightarrow ab=\dfrac{6760}{169}=40$

The coprime factor pairs of 40 are $(1,40)$ and $(5,8)$ . Since $(x,y)$ is an ordered pair, their reverses must also be counted.

$(a,b)$	$(x,y)$
$(1,40)$	$(13,520)$
$(40,1)$	$(520,13)$
$(5,8)$	$(65,104)$
$(8,5)$	$(104,65)$

Therefore, 4 such ordered pairs $(x,y)$ can be formed.

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Solution

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JIPMAT Past Year Questions (Topic-Wise)

The product of two positive integers $x$ and $y$ is 6760 and their HCF is 13. How many such pairs $(x, y)$ can be formed?