Learn

Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Exponent of Prime in n! (Legendre's Formula)

JEE Main asked Exponent of Prime in n! (Legendre's Formula) 2 times in 2 of the 108 shifts Lumi analysed, in 2023 and 2025. It belongs to Permutations and Combinations, in Binomial Theorem (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2023
last in 2025
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2023 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200’210’220.07’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20251 of 8
  • 20240 of 18
  • 20231 of 12
  • 20220 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Largest power of prime in factorial
  • Highest power of prime dividing factorial

Difficulty

Easy 2Medium 0Hard 0

1 of the 2 questions had a numerical answer.

Every question

All 2 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 2 Apr 2025, Shift 1 · Q6The largest n∈Nn\in\mathbf{N} such that 3n3^n divides 50!50! is :EasySingle correct
  2. 8 Apr 2023, Shift 1 · Q26The largest natural number nn such that 3n3^n divides 66!66! is ______________.EasyNumerical value

Shifts: 8 Apr 2023, Shift 1, 2 Apr 2025, Shift 1.

Same topic

Other ideas in Permutations and Combinations

Permutations and Combinations has 33 ideas JEE Main has asked; 20 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas