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Factorisation by Common Factors

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Question

Find the number of common factors of $10 p q$ , $20 q r$ , and $30 r p$ .

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Solution

$10 p q = 1 \times 2 \times 5 \times p \times q$
$20 q r = 1 \times 2 \times 2 \times 5 \times q \times r$
$30 r p = 1 \times 3 \times 2 \times 5 \times r \times p$
The common factors of $10 p q$ , $20 q r$ , and $30 r p$ are 1, 2, 5, and 10 $(∵ 2 \times 5)$

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