Exact
3628800
Factorial of 10
Answer
10! equals 3628800.
Decimal
3628800
Formula
10! = 10 × 9 × 8 × ... × 1 = 3,628,800
Worked steps
1
Definition
n! is the product of all positive integers up to n. For n = 10, multiply: 10! = 10 × 9 × 8 × ... × 1 = 3,628,800.
2
Calculator method
Type 10, press the x! button, press =. Result: 3628800.
3
Where it shows up
Factorials count the number of ways to arrange n distinct items. 10! = 3,628,800 means over 3.6 million orderings of 10 distinct items.
About this value
The factorial of 10 is 3628800. 10! = 3,628,800 — the number of ways to arrange 10 distinct items. Around 70! a typical calculator runs into floating-point overflow.
Frequently asked questions
What is factorial of 10?
Factorial of 10 equals 3628800 as an exact value, or 3628800 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.