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The largest n in N for which 7 n divides 101 is | null (Mathematics) | DivineJEE

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Mathematics

JEE Mains 2026 21st January Shift 2

Mathematics

The largest

\mathrm{n} \in \mathrm{N}

, for which

7^{\mathrm{n}}

divides 101!, is :

A

16

B

18

C

15

D

19

Correct Answer:

A

Explanation

Exponent of 7 in 101!

\\ \begin{aligned} & =\left[\frac{101}{7}\right]+\left[\frac{101}{7^{2}}\right]+\left[\frac{101}{7^{3}}\right]+\ldots \ldots \\ & =14+2=16 \end{aligned}

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