The largest n N , for which 7 n divides 101 , is : [2026]

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Solution

Q.
The largest $n \in N,$ for which $7^{n}$ divides $101!$ , is : [2026]

1 18

2 19

3 15

4 16

Ans.
(4)

$Exponent of 7 in 101!$

$= [\frac{101}{7}] + [\frac{101}{7^{2}}] + [\frac{101}{7^{3}}] + \dots$

$= 14 + 2 = 16$

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