JEE Main 202621 JanuaryEvening Shift
- Exam
- JEE Main
- Year
- 2026
- Date
- 21 January
- Shift
- Evening Shift
- Subject
- Mathematics
- Chapter
- Permutation and Combination
JEE Main 2026 · 21 January · Evening Shift · Mathematics · Permutation and Combination
The largest n ∈ N , for which 7^ n divides 101!, is :
The largest , for which divides 101!, is :
Options
- A16
- B15
- C18
- D19
Correct answer
A. 16
Step-by-step solution
Exponent of 7 in is:
\left\lfloor \frac{101}{7} \right\rfloor + \left\lfloor \frac{101}{7^2} \right\rfloor + \left\lfloor \frac{101}{7^3}\right\rfloor + \ldots = 14 + 2 = 16$.
\left\lfloor \frac{101}{7} \right\rfloor + \left\lfloor \frac{101}{7^2} \right\rfloor + \left\lfloor \frac{101}{7^3}\right\rfloor + \ldots = 14 + 2 = 16$.