Calculate exact factorials through 10,000 with BigInt, digit and trailing-zero counts, scientific previews and a readable factorial-growth chart.
01 / EXACT INTEGER FACTORIAL
Exact BigInt arithmetic, including every digit of 1000! and beyond. Choose Calculate so large work is not repeated while you type.
02 / EXACT VALUE & GROWTH
20! = 20 × 19!
Trailing zeros = ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …
Each next factorial multiplies the previous value by a larger integer, so digit growth accelerates. Zeros occur because each factor 5 pairs with a factor 2 to make 10; factors 25, 125 and higher powers contribute extra fives.
| n | Decimal digits in n! |
|---|---|
| 0 | 1 |
| 1 | 1 |
| 2 | 1 |
| 3 | 1 |
| 4 | 2 |
| 5 | 3 |
| 6 | 3 |
| 7 | 4 |
| 8 | 5 |
| 9 | 6 |
| 10 | 7 |
| 11 | 8 |
| 12 | 9 |
| 13 | 10 |
| 14 | 11 |
| 15 | 13 |
| 16 | 14 |
| 17 | 15 |
| 18 | 16 |
| 19 | 18 |
| 20 | 19 |
| n | n! |
|---|---|
| 0 | 1 |
| 1 | 1 |
| 2 | 2 |
| 3 | 6 |
| 4 | 24 |
| 5 | 120 |
| 6 | 720 |
| 7 | 5040 |
| 8 | 40320 |
| 9 | 362880 |
| 10 | 3628800 |
| 11 | 39916800 |
| 12 | 479001600 |
| 13 | 6227020800 |
| 14 | 87178291200 |
| 15 | 1307674368000 |
| 16 | 20922789888000 |
| 17 | 355687428096000 |
| 18 | 6402373705728000 |
| 19 | 121645100408832000 |
| 20 | 2432902008176640000 |
0! = 1 because an empty product equals one; this also keeps n! = n × (n−1)! consistent at n = 1. The Gamma function extends factorial-related ideas, but standard factorial here accepts only nonnegative integers.
Scientific notation shortens the value and is approximate when its mantissa is truncated. Digit count and trailing zero count are exact.
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Enter a nonnegative integer and select Calculate. Inspect exact digits, zeros and growth; expand very long integers only when needed or copy the full exact result.
Compute every digit through 10,000 factorial with exact BigInt arithmetic. Inspect leading and trailing digits, exact digit and zero counts, bounded multiplication steps and digit-growth data, then expand or copy the full integer when needed.
Factorial inputs and exact integers are computed locally on your device after you choose Calculate. Large digit strings are not uploaded or saved externally; expanding and copying the full result are deliberate local actions.
For a positive integer n, n! multiplies all integers from 1 through n. The recurrence is n! = n times (n−1)!. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
The product of no factors is the multiplicative identity, one. This empty-product convention also makes 1! = 1 × 0! consistent with the factorial recurrence.
The software limit is n = 10,000, whose factorial has 35,660 decimal digits. BigInt computes the full integer on submission, not every keystroke. Output over 300 digits is previewed and explicitly marked truncated; the full integer is still available for expansion or copying.
The exact count is floor(n/5) + floor(n/25) + floor(n/125) and so on. Every factor five pairs with a factor two to make ten. No scan of the entire factorial string is needed for this count.
The full BigInt integer, decimal digit count and trailing-zero count are exact. A shortened scientific mantissa is explicitly labeled a truncated approximation; it never replaces the exact full integer.
This standard factorial mode accepts only nonnegative integers. The Gamma function extends related concepts to some non-integer values, but that is a different calculation and is not silently substituted for n!.