Factorial Calculator: Instantly Find n! With Steps

How to Calculate Factorials and Use Them in Maths Problems

What is Factorial Calculator?

The Factorial Calculator helps you quickly find the value of n! (n factorial) for any non-negative integer. It is perfect for students learning discrete mathematics, combinatorics, or working on probability questions.

Simply enter a whole number and see the factorial answer instantly, along with a clear step-by-step multiplication breakdown. The tool is designed for mobile and desktop use to deliver instant clarity and accuracy.

Formula Behind Factorial Calculator

The factorial of a non-negative integer n, denoted as n!, is calculated as the product of all positive integers from n down to 1. Mathematically, n! = n × (n–1) × (n–2) × ... × 1, with the special case 0! = 1 by convention.

Factorial Conversion Table

n	n! (n factorial)	Stepwise Calculation
0	1	By definition: 0! = 1
3	6	3 × 2 × 1 = 6
5	120	5 × 4 × 3 × 2 × 1 = 120
7	5,040	7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
10	3,628,800	10 × 9 × ... × 1 = 3,628,800
15	1,307,674,368,000	15 × 14 ... × 1 = 1,307,674,368,000

Steps to Use Factorial Calculator

Enter the whole number n (e.g., 8 or 15) into the box.
Click "Calculate".
Instantly see accurate results and the step-by-step multiplication below.

Why Use Vedantu’s Factorial Calculator?

Vedantu’s tool saves time and removes guesswork for factorial questions in maths, permutations, and combination topics, especially for large values of n.

Each calculation includes the exact steps, ideal for building mathematical understanding and for use in exams or competitive test prep. The clear stepwise output helps students link the answer to classroom formulas easily.

Applications of Factorial Calculator

Factorials are used to count total arrangements, solve permutation and combination problems, and compute probabilities in board games or real-world tasks such as seat arrangements.

The calculator is also handy for science, coding, and computer algorithms, including recursive programming, tree structures, and various logic puzzles commonly featured in mathematics olympiads or coding competitions. To deepen your understanding, explore topics like permutations and combinations or prime numbers on Vedantu.

For more number tools, try the HCF Calculator, algebra theory topics, or learn about multiples of numbers to strengthen your maths foundations.

Developed and reviewed by certified maths educators, Vedantu’s calculator is based on school board standards and checked for accuracy. Trusted by students and teachers alike, it supports deep learning and fast revision for exams and daily practice.

FAQs on Factorial Calculator: Instantly Find n! With Steps

1. What is a factorial in mathematics?

A factorial, denoted by the symbol '!', is the product of all positive integers less than or equal to a given positive integer. For example, 5! (5 factorial) is 5 × 4 × 3 × 2 × 1 = 120. It's a fundamental concept in combinatorics and probability, used to count arrangements and possibilities.

2. How do I calculate the factorial of a number?

To calculate the factorial of a number (n!), you multiply that number by every positive integer smaller than it, down to 1. For instance, to find 6!, you would calculate 6 × 5 × 4 × 3 × 2 × 1 = 720. The factorial of 0 (0!) is defined as 1.

3. What is the factorial of 0 (0!)?

The factorial of 0, denoted as 0!, is defined as 1. This is a convention established to maintain consistency in mathematical formulas and theorems involving factorials.

4. What are some real-world applications of factorials?

Factorials are used extensively in various fields: Probability calculations (like determining the likelihood of specific outcomes), permutations (arranging objects in different orders), combinations (selecting objects from a group without regard to order), and in certain computer science algorithms.

5. How is the factorial used in permutations and combinations?

Factorials are fundamental to calculating permutations and combinations. Permutations deal with the number of ways to arrange items in order, while combinations focus on selecting items without considering their order. The formulas for both involve factorials.

6. What is the factorial formula?

The factorial formula is expressed as n! = n × (n-1) × (n-2) × ... × 2 × 1, where n is a non-negative integer. This means you multiply n by every positive integer below it until you reach 1.

7. Why is the factorial important in discrete mathematics?

Factorials are a cornerstone of discrete mathematics because they provide a way to count the number of arrangements or selections of discrete objects. This is crucial for solving problems in combinatorics, graph theory, and other areas of discrete mathematics.

8. How do I calculate large factorials?

Calculating very large factorials by hand is impractical. Use a calculator or computer program designed for this purpose. Many online factorial calculators are available, providing quick and accurate results for even very large numbers.

9. What is the difference between permutation and combination?

Permutations consider the order of selection, while combinations do not. For example, if you have three letters (A, B, C) and want to arrange two, the permutations are AB, BA, AC, CA, BC, CB (6 ways). The combinations are just AB, AC, BC (3 ways), as the order doesn't matter.

10. Where can I find a free online factorial calculator?

Vedantu provides a free online factorial calculator that allows you to quickly and easily calculate the factorial of any non-negative integer. The calculator also shows the step-by-step calculation, which can aid in understanding the concept.

11. What if I enter a negative number into a factorial calculator?

Factorials are only defined for non-negative integers. If you try to calculate the factorial of a negative number, most calculators will show an error message or indicate that the input is invalid. The factorial function is not defined for negative numbers.

12. How are factorials used in probability problems?

Factorials are essential in probability for calculating the number of possible outcomes in various scenarios. For example, when determining the probability of arranging a specific sequence of cards from a deck, factorials are used to find the total number of possible arrangements (the denominator in the probability fraction).