Factorial Calculator

Introduction to the Factorial Calculator

The Factorial Calculator computes n! for any non-negative integer using the formula: n! = n x (n-1) x (n-2) x ... x 2 x 1, with 0! defined as 1. It is one of the most-used building blocks in permutations, combinations, probability, binomial expansion and Taylor series across Indian school and college maths.

Indian Class 11 and 12 students under CBSE, ICSE and state boards encounter factorials in NCERT chapter Permutations and Combinations, where formulas like nPr = n!/(n-r)! and nCr = n!/[r!(n-r)!] dominate the exercise sets. JEE Main, JEE Advanced, NDA, CDS and BITSAT regularly include factorial-heavy questions worth 8 to 12 marks per paper.

You enter a single non-negative integer n. The tool returns n! in full digits, scientific notation for large values, and a step-by-step breakdown. It handles n up to 170 within standard floating-point range and uses big-number arithmetic for higher values.

Who Should Use This Factorial Calculator

CBSE Class 11 students like Kavya in Delhi solving NCERT Chapter 7 Permutations and Combinations need this to verify homework answers quickly. JEE aspirants like Arjun in Kota practicing binomial theorem and probability sums use it to cross-check intermediate steps in 4-mark problems. Engineering students like Rohan in Bengaluru working on discrete math, combinatorics and algorithm analysis (Big-O notation involves n!) use it routinely. Statistics students like Priya in Pune computing Poisson distribution probabilities, where e raised to power negative lambda x lambda^k / k! appears, use it daily. Competitive coders like Manish in Hyderabad on Codeforces and CodeChef use it to verify formulas before writing brute-force solutions.

Tips for Factorial Problems

Smart Factorial Tips

Memorize factorials up to 10! by heart: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800. This saves 30 to 45 seconds per JEE question.

Simplify before computing. For nCr, divide n! by (n-r)! to cancel terms. Example: 10C2 = 10!/(8! x 2!) becomes (10 x 9)/2 = 45 without ever computing 10! fully.

Watch for factorials in disguise. The Indian board favourite "arrangements of MISSISSIPPI" is 11!/(4! x 4! x 2!), not just 11!. Always look for repeated letters or grouped objects.

For probability sums using Poisson or normal approximations, use Stirling's formula: n! is approximately equal to sqrt(2 pi n) x (n/e)^n for large n. This is in the NCERT supplementary syllabus for some boards.

Never compute n! beyond 170 in standard programs. Java long and Python int handle it but spreadsheets like Excel overflow at 171!. Use big-number libraries or this calculator for higher values.

Formula Explanation

Core Factorial Formula

n! = n x (n-1) x (n-2) x ... x 2 x 1

Where:

• n = non-negative integer
• • 0! = 1 by definition
• • 1! = 1
• • The product runs from n down to 1

Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720. Used in arrangements: number of ways to seat 6 people in a row at a wedding in Lucknow is 6! = 720.

Factorial Quick Reference Table

n	n!	Digits	Example Use
5	120	3	Arranging 5 books on a shelf
7	5,040	4	Days in a week permutations
10	3,628,800	7	Seating 10 guests at a dinner
15	1.31 x 10^12	13	IPL team batting order combos
20	2.43 x 10^18	19	20-team tournament fixtures

Real-World Example

Example: Ishita's JEE Permutation Problem in Mumbai

Meet Ishita, an 18-year-old Class 12 student from Mumbai preparing for JEE Main 2026. Her mock test asks: How many distinct arrangements of the letters in ENGINEERING are possible?

Step 1: She counts the letters: 11 total. Repeated: E appears 3 times, N appears 3 times, I appears 2 times, G appears 2 times, R appears 1 time.

Step 2: She enters values into the formula: 11!/(3! x 3! x 2! x 2! x 1!) = 39,916,800/(6 x 6 x 2 x 2 x 1) = 39,916,800/144.

Step 3: The calculator returns 11! = 39,916,800 and divides by 144 to give 277,200.

Result: 277,200 distinct arrangements. Ishita matches this with the JEE answer key and confirms her understanding, gaining 4 marks on this question type in the actual exam.

Frequently Asked Questions About Factorials

Common questions Indian students ask about factorials include why 0! equals 1, how to compute factorials of negative numbers and fractions (using the Gamma function), the largest factorial that fits in a 64-bit integer, applications of factorial in binomial expansion and probability, and how factorial growth compares with exponential growth. The answers below cover each of these in detail with NCERT-aligned explanations.