How to Simplify Factorials

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A factorial, such as four factorial, means that the result is four times three times two times one. Find out how to simplify factorials when they're used in fractions with help from a tutor in this free video on math lessons and study tips.

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Let's look at simplifying factorials. So first, a basic factorial. If we had 4 factorial, this symbol just means factorial, you read it as factorial. And what it means is 4 times 3 times 2 times 1. It means multiply that number by each integer below it; each positive integer below it. So 4 factorial, 4 times 3 times 2 times 1. So let's simplify. If we had, let's say, 5 factorial over 3 factorial, how do we simplify that? We can't just subtract or divide; it doesn't become five-thirds, it doesn't become 5 minus 3. What we do is, if you take a look at it, it's 5 times 4 times 3 times 2 times 1, over 3 times 2 times 1. So what we wind up getting is the threes, the twos and the ones will cancel out, and so you wind up actually with just 5 times 4, which is 20. So 5 factorial over 3 factorial simplifies to be 20.

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