Why Use This Tool?
Factorials (n! = n × (n−1) × … × 1) explode fast — 69! overflows a regular calculator's floating-point precision. This tool uses big-integer arithmetic for exact results up to 500!, which is precisely the range combinatorics and probability problems ask for.
The modulo panel computes the remainder after division — the operation behind 'every 7th item', clock arithmetic, and hash bucketing.
How It Works
- Enter n for an exact factorial, up to 500.
- Use the modulo panel for remainder questions like 'what's left after dividing 100 by 7'.
- Copy exact digit-perfect results into your homework or code.
Frequently Asked Questions
What is a factorial?
The product of all positive integers up to n: 5! = 5 × 4 × 3 × 2 × 1 = 120. It counts the ways to arrange n items, which is why it explodes so fast.
Why do regular calculators fail at large factorials?
They use floating-point numbers that overflow around 69!. This tool uses big-integer arithmetic, so 500! is exact to all of its 1,135 digits.
What does the modulo operation do?
It returns the remainder after division: 100 mod 7 = 2. It's the operation behind even/odd checks, clock arithmetic, and cyclic scheduling.
Tips & Things to Watch
- 0! is defined as exactly 1 — the empty-product convention.
- Factorials power permutations: n! counts the ways to line up n items.
- Modulo with a negative dividend still returns a non-negative result here.