Factorial as Product of Three Factorials/Examples/16
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Example of Factorial as Product of Three Factorials
- $16! = 14! \times 5! \times 2!$
Proof
| \(\ds 16!\) | \(=\) | \(\ds 14! \times 15 \times 16\) | Definition of Factorial | |||||||||||
| \(\ds \) | \(=\) | \(\ds 14! \times 3 \times 5 \times 2^4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 14! \times \left({2 \times 3 \times 2^2 \times 5}\right) \times 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 14! \times 5! \times 2!\) |
$\blacksquare$
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $16$