# If a = (22 × 33 × 54) and b

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 (ab) = Product of smallest power of each common prime factor in the numbers

$=2^{2} \times 3^{2} \times 5$

= 180