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Mathematics · Permutations and Combinations

JEE Main 2026 — 21 January, Evening Shift — Question 20

The largest n∈N\mathrm{n} \in \mathrm{N}, for which 7n7^{\mathrm{n}} divides 101!101!, is :

  1. Option A:

    1616

    Correct
  2. Option B:

    1818

  3. Option C:

    1515

  4. Option D:

    1919

Answer: A

Step-by-step solution

Exponent of 7 in 101! =[1017]+[10172]+[10173]+……=\left[\frac{101}{7}\right]+\left[\frac{101}{7^{2}}\right]+\left[\frac{101}{7^{3}}\right]+\ldots \ldots =14+2=16=14+2=16

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
21 January, Evening Shift
Subject
Mathematics
Chapter
Permutations and Combinations
Topic
Exponent Of Prime in n!
The largest n in N , for which 7 n divides 101! , is : | JEE Main 2026 PYQ with Solution · DhiX AI