One number does not fit into the given factorial series.

Identify it. 3, 6, 24, 120, 720, 800

The correct answer is 800.

Let's analyze the pattern in the given factorial series:

3, 6, 24, 120, 720, 800

The series is based on the factorials of consecutive integers starting from 3:

$3!=3\times 2\times 1=6$

$4!=4\times 3\times 2\times 1=24$

$5!=5\times 4\times 3\times 2\times 1=120$

$6!=6\times 5\times 4\times 3\times 2\times 1=720$

$7!=7\times 6\times 5\times 4\times 3\times 2\times 1=5040$

Alternatively, looking at the multiplicative progression between successive terms:

$6\times 4=24$

$24\times 5=120$

$120\times 6=720$

$720\times 7=5040$

In the given sequence, the last number is 800 instead of 5040 (or 7!), which does not follow the factorial rule.

Therefore, 800 is the number that does not fit into the series.