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Product Law

If 6! = 2p ...

Question

If 6! = $2^{p} 3^{q} 5^{r}$ , then P + q + r =

A

6

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B

7

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C

8

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D

9

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Solution

The correct option is C 7
$6! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 = 720$
$2^{4} \times 3^{2} \times 5$
Given 6! = $2^{4} \times 3^{2} \times 5 = 2^{p} 3^{q} 5^{r}$
p = 4, q = 2 , r = 1
p + q + r = 4 + 2 + 1 = 7

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