How to Divide Factorials

••• Photo by Miguel Ugalde,

The term factorial is a mathematical expression that represents taking a non-negative integer and multiplying it by all positive integers less than the original number. For example, the factorial of 5 is 5 * 4 * 3 * 2 * 1 = 120. The abbreviation n! is used to denote the factorial of the positive integer n. It's easy to see that the factorial n! can be quite large even for small values of n so the division of two factorials can look time-consuming at first. However, there is a nice little trick that makes this computation much quicker and easier.

    Write down the two factorials you wish to divide in fractional form. For instance, if you wish to divide 11! by 8!, on your paper write 11! / 8!.

    Determine whether the numerator or denominator is larger. In this example, the numerator 11! is larger since 11 > 8.

    Expand the factorial representation of this larger number until you arrive at the smaller number. Here, you would have 11! = 11 * 10 * 9 * 8! as your expansion.

    Simplify your fraction, canceling any like terms that are present in both the numerator and denominator. We have 11! / 8! = (11 * 10 * 9 * 8!) / 8! = (11 * 10 * 9) / 1 since 8! can be factored out of both the numerator and denominator.

    Perform any remaining multiplication or division if necessary. In your example, (11 * 10 * 9) / 1 = 990.

    Things You'll Need

    • Paper
    • Pencil or pen

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Photo Credits

  • Photo by Miguel Ugalde,