5040 is Product of Consecutive Numbers in Two Ways

Theorem

$5040 = 7 \times 6 \times 5 \times 4 \times 3 \times 2 = 10 \times 9 \times 8 \times 7$

Proof

Follows from Factorial as Product of Two Factorials:

$10! = 6! \times 7!$

and so:

$\dfrac {10!} {6!} = 10 \times 9 \times 8 \times 7 = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$

Hence the result.

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5040$