Given that $(p + 3)$ is the highest common factor of 81 and 108, find the value of $p$ .

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Solution

The correct option is D
24

Prime factorisation of 81 and 108:

81 = 3 $\times$ 3 $\times$ 3 $\times$ 3
108 = 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 3

$∴$ The highest common factors is 3 $\times$ 3 $\times$ 3 = 27

Given, HCF of 81 and 108 is $(p + 3)$ .
$∴ p + 3 = 27$
$\Rightarrow p = 24$

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