Question:
If $a=\left(2^{2} \times 3^{3} \times 5^{4}\right)$ and $b=\left(2^{3} \times 3^{2} \times 5\right)$, then $\operatorname{HCF}(a, b)=$ ?
(a) 90
(b) 180
(c) 360
(d) 540
Solution:
(b) 180
It is given that:
$a=\left(2^{2} \times 3^{3} \times 5^{4}\right)$ and $b=\left(2^{3} \times 3^{2} \times 5\right)$
∴ HCF (a, b) = Product of smallest power of each common prime factor in the numbers
$=2^{2} \times 3^{2} \times 5$
= 180