Find the HCF of the following algebraic expressions.
$7 p, 14 p^{2}$ and $21 p^{2} q$

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Solution

We first factorize the given algebraic expressions $7 p, 14 p^{2}$ and $21 p^{2} q$ as shown below:

$7 p = 7 \times p 14 p^{2} = 2 \times 7 \times p \times p 21 p^{2} q = 3 \times 7 \times p \times p \times q$

The common factors of $7 p, 14 p^{2}$ and $21 p^{2} q$ are $7$ and $p$ , therefore, the HCF is:

$7 \times p = 7 p$

Hence, the HCF of $7 p, 14 p^{2}$ and $21 p^{2} q$ is $7 p$ .

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