If 2009 = $p^{a} . q^{b}$ where p and q are prime numbers then find the value of p + q

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2009

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Solution

The correct option is B 48
Given $2009 = p^{a} q^{b}$ ...(i)
Where p and q are prime numbers
We know that $2009 = 7 \times 7 \times 41 = 7^{2} \times 41^{1}$ ...(ii)
Comparing equation (1) and (2) we get
$p = 7, q = 41, a = 2 a n d b = 1$
$∴ p + q = 7 + 41 = 48$

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