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This question already has an answer here:

Is it just a coincidence that 10! = 3! · 5! · 7! and 6! = 3! · 5! or are factorials somehow related to primes in terms of prime factorial factors?

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marked as duplicate by Arnaud D., Shailesh, Robert Soupe, астон вілла олоф мэллбэрг, user223391 Nov 20 '16 at 3:30

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    $\begingroup$ How about you take a look at this question? $\endgroup$ – Hungry Blue Dev Nov 19 '16 at 20:42
  • $\begingroup$ Thanks a lot, I will have a look at it. $\endgroup$ – David Nov 19 '16 at 21:03
  • $\begingroup$ It doesn't quite answer my question unfortunately. $\endgroup$ – David Nov 19 '16 at 21:11
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    $\begingroup$ Well, $10! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10$. So just $3! \times 5!$ falls short in part because it lacks $7$. $\endgroup$ – Mr. Brooks Nov 19 '16 at 22:40