If integer k is equal to the sum of all even multiples of 15 between 295 and 615, what is the greatest prime factor of k?


The above question is from MGMAT CAT. The solution seems confusing.

The way I thought was as follows:

Multiples of 15 between 295 and 615 are all the multiples of 15 between 300 and 600


Sum = Avg * N

Avg: (Last + First)/2 = 600+300/2 = 450

N: (L-F)/Multiple + 1

(600-300)/15 + 1

300/15 + 1

= 21

Sum = 450 * 21

Prime Factors of 450 = 3.3.5.5.2 and Prime Factors of 21 = 7.3

Greatest Prime Factor = 7

Where did I go wrong?