A prime number is a natural number, greater than one, that can only be divided by 1 and itself.
The number 309600 can be evenly divided by 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 40 43 45 48 50 60 72 75 80 86 90 96 100 120 129 144 150 160 172 180 200 215 225 240 258 288 300 344 360 387 400 430 450 480 516 600 645 688 720 774 800 860 900 1,032 1,075 1,200 1,290 1,376 1,440 1,548 1,720 1,800 1,935 2,064 2,150 2,400 2,580 3,096 3,225 3,440 3,600 3,870 4,128 4,300 5,160 6,192 6,450 6,880 7,200 7,740 8,600 9,675 10,320 12,384 12,900 15,480 17,200 19,350 20,640 25,800 30,960 34,400 38,700 51,600 61,920 77,400 103,200 154,800 and 309,600, with no remainder.
Since 309,600 cannot be divided by just 1 and 309,600, it is not a prime number.