If $n = 20! + 17$ , then $n$ is divisible by which of the following ?
I. $15$
II. $17$
III. $19$

None

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I only

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II only

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I and II

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II and III

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Solution

The correct option is C II only
Given:
$n = 20! + 17$
$= 17 [\frac{20!}{17} + 1]$
Since $\frac{20!}{17}$ is a whole number, so it is divisible by $17$
Hence, the answer is $17.$

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