Factorial/Examples/52

Example of Factorial

The number of ways there are to shuffle a $52$-card deck is given by:

$52! = 806 \ 58175 \ 17094 \ 38785 \ 71660 \ 63685 \ 64037 \ 66975 \ 28950 \ 54408 \ 83277 \ 82400 \ 00000 \ 00000$

Prime Factors of $52!$

The prime decomposition of $52!$ is given as:

$52! = 2^{49} \times 3^{23} \times 5^{12} \times 7^8 \times 11^4 \times 13^4 \times 17^3 \times 19^2 \times 23^2 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47$

Proof

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Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials: Exercise $1$