36 of them.
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7*5*4*3*2 Is the longest factor string of 840
The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.
You will know because all of the numbers are prime.
2 x 2 x 2 x 3 x 5 x 7
2 x 2 x 2 x 3 x 5 x 7