Question

If $2028$ is the product of two natural numbers having two digits each and $13$ is their highest common factor, then the numbers are

• A. $26,78$
• B. $13,156$
• C. $36,58$
• D. $39,52$

Answer 1

The correct option is D $39,52$

Let $x$ and $y$ be two numbers.
Given $2028=x\times y$
Also known that HCF of $x$ and $y$ is $13$.
We know H.C.F $\times$ L.C.M $=2028$
Hence, $LCM=156$, but we want a $2$ digit number. $2028$ can be expressed differently such as,
$2028=13\times 156$
$2028=26\times 78$ ; here, HCF of $26$ and $78$ is $26$ itself.
$2028=39\times 52$, where the HCF of

$52$ and $39$ is $13$.
Hence, the numbers are $39$ and $52$.