Prime factorization of 840 show how

It's best when doing the prime factorization if the numbers are as close as possible,

So instead of doing 420 x 2 which are far apart, I will do 84 x 10 which are closer together.

84 = 7 x 12 = 7 x 3 x 4 = 7 x 3 x 2 x 2 or 2² x 3 x 7 (I put the in order from smallest base to largest)

10 = 2 x 5

Now lets combine the two: 2³ x 3 x 5 x 7 and that is your prime factorization of 840