Calculate n factorial as an exact whole number, including 0!, and understand the multiplication behind the result.
5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.
Multiply every positive whole number from 5 down to 1.
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How to Use the Factorial Calculator
Enter a whole number from 0 to 500. The result shows the exact product and two useful checks: the number of digits and the number of trailing zeros. For large results, scroll within the result area.
Factorials grow rapidly. The tool uses whole-number arithmetic, so it does not round the answer.
What Does n! Mean?
The exclamation mark means multiply all positive whole numbers from n down to 1. For a positive n, n! = n × (n − 1)!. The special starting value 0! = 1 makes that rule consistent.
Worked Example: 5 Factorial
Start at 5 and multiply downward: 5 × 4 = 20, 20 × 3 = 60, 60 × 2 = 120, and 120 × 1 = 120. Therefore 5! = 120. This also counts the distinct ways to arrange five different items in order.
Why Do Factorials End in Zeros?
Each trailing zero comes from a factor of 10, or one factor of 2 paired with one factor of 5. Factorials contain more 2s than 5s, so count the factors of 5. The count is ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + … until the quotient is zero.
Common Factorial Mistakes
Is 0! equal to 0?
No. The standard factorial definition sets 0! = 1.
Can I use a negative number or decimal?
This calculator evaluates the standard elementary factorial for nonnegative whole numbers. Other extensions require different definitions.
Is n! the same as n × n?
No. n! multiplies every positive whole number up to n; n × n uses only n twice.
Factorial Calculator FAQs
What is 10 factorial?
10! = 3,628,800.
Why is 0 factorial 1?
The empty product is defined as 1, which also keeps n! = n × (n − 1)! consistent at n = 1.
How large a factorial can this tool calculate?
It calculates exact factorials for whole numbers from 0 through 500.
Editorial review
SolverCalc names Prof. Dr. Khalil Mudassar as its educational reviewer. The calculation follows the standard factorial definition and can be checked against the references below.
Sources
View references
Disclaimer
For educational use. Check your class or textbook convention when the problem defines a different range, sequence index, or notation.