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Factorial Calculator
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Home / Math / Factorial Calculator
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Add this free factorial calculator to your website or blog.
This is defined this way because it makes mathematical formulas work. The number of ways to arrange 0 items is 1 (do nothing). It's also necessary for the binomial theorem and other formulas to work correctly.
Factorials increase incredibly quickly. 10! = 3,628,800. 20! = 2,432,902,008,176,640,000. By 70!, you're already past the number of atoms in the universe!
If you have 5 books, there are 5! = 120 different ways to arrange them on a shelf. In general, n items can be arranged in n! ways.
The most common error. Remember: 0! = 1, not 0. It's a special definition that makes math work cleanly.
5! ≠ 5^5. Factorial means 5×4×3×2×1 = 120. Exponent means 5×5×5×5×5 = 3,125. Very different!
Factorials are only defined for non-negative integers. (-5)! is undefined.