Divisibility of Product of Consecutive Integers/Examples

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 $15$

\(\ds 11 \times 12 \times 13 \times 14 \times 15\)

\(=\)

\(\ds 360 \, 360\)

\(\ds \)

\(=\)

\(\ds 3003 \times 120\)

\(\ds \)

\(=\)

\(\ds \binom {15} 5 \times 11 \times 12 \times 13 \times 14 \times 15\)