Find the value of p and q, so that the prime factorisation of 2520 can be expressed as $2^{3} \times 3^{p} \times q \times 7$ .

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Solution

$2520 = 2^{3} \times 3^{p} \times q \times 7$
Since
$2520 = 2^{3} \times 3^{2} \times 5 \times 7$
On comparing $p = 2, q = 5$

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2 Q + 3 P = \frac{3 P - Q}{2 R}

R = - 2

Q = 1

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