If $a = 2^{3} 3^{5}, b = 3^{2} 2^{5}$ , then find the $H C F$ of $a$ and $b$ .

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Solution

$a = 2^{3} 3^{5} = (2 \times 2 \times 2) \times (3 \times 3 \times 3 \times 3 \times 3)$

$b = 2^{5} 3^{2} = (2 \times 2 \times 2 \times 2 \times 2) \times (3 \times 3)$

$H C F (a, b) = (2 \times 2 \times 2 \times) (3 \times 3) = 2^{3} \times 3^{2} = 8 \times 9 = 72$

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