Factorial Division

Number Theory Level 1

Find the value of x x satisfying x ! 23 ! = 4 ! \dfrac{x!}{23!} = 4! .

Notation : ! ! denotes the factorial function. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 24.

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Vincent Jordaan by Vincent Jordaan , 25, South Africa

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2 solutions

Ashish Menon
May 23, 2016

x ! 23 ! = 4 ! x ! = 24 × 23 ! x ! = 24 ! x = 24 \begin{aligned} \dfrac{x!}{23!} & = 4!\\ x! & = 24 × 23!\\ x! = 24!\\ x = \color{#69047E}{\boxed{24}} \end{aligned}

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Vincent Jordaan
May 14, 2016

Relevant wiki: Factorials

x ! 23 ! \frac{x!}{23!} = 4!

To approach this problem you only need to know the very basics of factorials.

First off one must note that you do not need to find the factorial of 23.

Merely find 4! (which is 24).

Next take the 23! over to the right hand side, to give x! = 23!*24

You will then notice that this equals merely 24! (By using n! = (n-1)! * n)

Thus, x = 24

1 Helpful 0 Interesting 1 Brilliant 0 Confused

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