Exact
120
Factorial of 5
Answer
5! equals 120.
Decimal
120
Formula
5! = 5 × 4 × 3 × 2 × 1 = 120
Worked steps
1
Definition
n! is the product of all positive integers up to n. For n = 5, multiply: 5! = 5 × 4 × 3 × 2 × 1 = 120.
2
Calculator method
Type 5, press the x! button, press =. Result: 120.
3
Where it shows up
Factorials count the number of ways to arrange n distinct items. 5! = 120 means 120 different orderings of 5 books on a shelf.
About this value
The factorial of 5 is 120. 5! = 120 is the smallest factorial that exceeds 100 — used in early combinatorics problems.
Frequently asked questions
What is factorial of 5?
Factorial of 5 equals 120 as an exact value, or 120 as a decimal. The exact form is what you'd typically write in exam working; the decimal is what your calculator displays.
Why is 0! equal to 1?
By convention. The empty product (multiplying no numbers together) is 1, the multiplicative identity. This convention makes formulas like nCr(n, 0) = 1 and nPr(n, 0) = 1 hold without special cases.
How fast does factorial grow?
Very fast. 5! = 120, 10! ≈ 3.6 million, 15! ≈ 1.3 trillion. Most scientific calculators hit floating-point overflow somewhere around 170! — values bigger than that show as Infinity or scientific notation only.
Where is factorial used?
Mostly in counting problems — permutations (n!) and combinations (nCr, nPr). Also in series expansions like sin(x) = x − x³/3! + x⁵/5! − …, and in probability density functions for discrete distributions.