Product of NN Consecutive Integers Divided by NN

1 is divisible by 1.
2×32\times 3 is divisible by 2.
4×5×64\times5\times6 is divisible by 3.
7×8×9×107 \times 8 \times 9 \times 10 is divisible by 4.
11×12×13×14×1511 \times 12 \times 13 \times 14 \times 15 is divisible by 5.

True or False?

The product of any NN consecutive integers must be divisible by N.N.

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