There are many more than seven, but here's what you asked for.
2 x 420
3 x 280
4 x 210
5 x 168
6 x 140
7 x 120
8 x 105
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7*5*4*3*2 Is the longest factor string of 840
36 of them.
The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.
3 x 5 x 7 x 8 2 x 6 x 7 x 10
2 x 2 x 2 x 3 x 5 x 7