Question

H.C.F of $a^2{b}^3$ and $a^3{b}^2{d}^7$ is $a^2{b}^2$. What is their H.C.F

• A. $a^2{b}^2$
• B. $a^2{b}^3$
• C. $a^3{b}^2{d}^7$
• D. None of the above

Answer 1

The correct option is A

$a^2{b}^2$

H.C.F is called highest common factor and G.C.D is called greatest common divisor. H.C.F and G.C.D are same for any expressions.
For finding the H.C.F or G.C.D of two polynomial, we look for the lowest power of each variable in the given polynomials.
Lowest power of $a$ in the given polynomials = 2
Lowest power of $b$ in the given polynomials = 2
Lowest power of $d$ in the given polynomials = 0

$\therefore$ H.C.F ( or G.C.D) = $a^2{b}^2$