Divisibility of Product of Consecutive Integers/Examples
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Examples of Divisibility of Product of Consecutive Integers
Product of $5$ to $8$
\(\ds 5 \times 6 \times 7 \times 8\) | \(=\) | \(\ds 1680\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 70 \times 24\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \binom 8 4 \times 1 \times 2 \times 3 \times 4\) |
Product of $10$ to $13$
\(\ds 10 \times 11 \times 12 \times 13\) | \(=\) | \(\ds 17 \, 160\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 715 \times 24\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \binom {13} 4 \times 1 \times 2 \times 3 \times 4\) |
Product of $4$ to $8$
\(\ds 4 \times 5 \times 6 \times 7 \times 8\) | \(=\) | \(\ds 6720\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 56 \times 120\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \binom 8 5 \times 1 \times 2 \times 3 \times 4 \times 5\) |
Product of $11$ to $15$
\(\ds 11 \times 12 \times 13 \times 14 \times 15\) | \(=\) | \(\ds 360 \, 360\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3003 \times 120\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \binom {15} 5 \times 11 \times 12 \times 13 \times 14 \times 15\) |