Скачать или смотреть L3 | Permutation and Combination Class 11th | Exponents of Prime in n factorial | Mains & Advanced

Hello Future IITians and NITians! Welcome back to Integron Maths. 🚀

This is the third lecture in our comprehensive series on Permutations and Combinations for JEE Mains and Advanced. In this crucial session, we'll master the concept of finding the Exponent of a Prime 'p' in n-factorial (n!), also famously known as Legendre's Formula.

This is a frequently tested topic in JEE and other competitive exams, and understanding it is key to solving complex problems involving factorials.

📚 In This Lecture, We Will Cover:
What is Legendre's Formula? A clear, from-the-basics explanation of how to find the highest power of a prime number that divides n!.

The Core Formula: We'll break down the formula exponents of prime 'p' in n! ensuring you understand every part of it.

Exponent of Composite Numbers: Learn the trick to find the highest power of any composite number (like 6, 10, 12, etc.) in n! by breaking it down into its prime factors.

Problem-Solving Session: We will solve 9 challenging problems, including Previous Year Questions (PYQs) from JEE Main & Advanced, to solidify your concepts and boost your confidence.


👨‍🏫 Your Instructor:
Shubham Kumar (M.Sc in Mathematics and Scientific Computing)



▶️ Check Out My Previous Playlists:

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Relations 11th: [   • Relations Class 11th | Complete Lecture Se...  ]

Relations 12th:[    • Relations Class 12th | Complete Lecture Se...  ]

Binomial Theorem: [   • Binomial Theorem Complete Series | JEE Mai...   ]

🎯 Who Should Watch This Video?
Students preparing for JEE Main & Advanced 2026 & 2027.

Class 11 students starting their Permutations and Combinations chapter.

Aspirants of other engineering entrance exams like BITSAT, WBJEE, MHT CET, etc.

Anyone who wants to build a strong foundation in Number Theory for competitive programming or math olympiads.

Thank you for choosing Integron Maths for your JEE preparation. If you learn something new, don't forget to support the channel!



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Let's crack JEE together!


00:00 - Introduction & Intuition behind the Concept

00:36 - Exponents of Prime 'p' in n! (Legendre's Formula)

05:11 - Basic Problem on Legendre's Formula

16:36 - Problem 1: Exponents of 2 in 25!

17:49 - Problem 2: Largest 'n' such that 3 n divides 50! (JEE Main 2025)

19:49 - Problem 3: Trailing Zeros Problem

24:58 - Problem 4: Exponents of Composite Numbers in n!

29:28 - Problem 5: Finding the largest power of a number that divides 22!

32:21 - Problem 6: Ten's Digit in a Factorial Sum

36:43 - Problem 7: JEE Main 2024 PYQ

42:33 - Problem 8: How many positive integers 'n' exist such that n! has exactly 25 trailing zeros?







Tags

#JEEMain2026 #JEEAdvanced #PermutationAndCombination #IITJEE #LegendresFormula #ExponentsOfPrime #Factorial #NumberTheory #JEEMaths #JEETricks #JEEPYQs #Class11Maths #MathsForJEE #IntegronMaths #JEE2027