Challenging P6

6, 24, 60, 120, 210, ?

What follows after 210 ?


Factors of 6 --> 1, 2, 3, 6
1st number --> 6=  2 x 3
                          = (1 x 2) x (1 + 2)
= 2 x (2 x 3)/2 = 1 x 2 x 3

Factors of 24 --> 1, 2, 3, 4, 6, 8, 12, 24
2nd number --> 24 = 4 x 6
                              = (2 x 2) x (1 + 2 + 3)
= 4 x (3 x 4)/2 = 2 x 3 x 4

Factors of  60 --> 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
3rd number --> 60 = 6 x 10
                             = (3 x 2) x (1 + 2 + 3 + 4)
= 6 x (4 x 5)/2 = 3 x 4 x 5

Factors of 120 --> 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
4th number --> 120 = 8 x 15
                               = (4 x 2) x (1 + 2 + 3 + 4 + 5)
= 8 x (5 x 6)/2 = 4 x 5 x 6

Factors of 210 --> 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
5th number --> 210 = 10 x 21
                               = (5 x 2) x (1 + 2 + 3 + 4 + 5 + 6)
= 10 x (6 x 7)/2 = 5 x 6 x 7

6th number -->  (6 x 2) x (1 + 2 + 3 + 4 + 5 + 6  + 7)
                     = 12 x (7 x 8)/2
= 6 x 7 x 8
                     = 336

The next number is 336.