Question

If p, m and n are prime numbers none of which is equal to the other two what is the greatest common factor of $24p{m}^2{n}^2,9pm{n}^{2}and36p{\left(mn\right)}^3$?

• A. 3pmn
• B. $3p^2{m}^2{n}^2$
• C. $3pm{n}^2$
• D. $3pm{n}^3$

Answer 1

The correct option is C $3pm{n}^2$

$24p{m}^2{n}^2,9pm{n}^{2}and36p{\left(mn\right)}^3$
$24p{m}^2{n}^2=2\times 2\times 2\times 3\times p\times m\times m\times n\times n$
$9pm{n}^2=3\times 3\times p\times m\times n\times n$
$36p{\left(mn\right)}^3=2\times 2\times 3\times 3\times p\times m\times m\times m\times n\times n\times n$
$\therefore RequiredH.C.F=3pm{n}^2$