How many numbers between 300 and 500 are divisible by 13?

The multiples of 13 in this range form the AP 312, 325, ..., 494 (13 * 24 = 312 and 13 * 38 = 494). From 494 = 312 + (n - 1)13 we get 182 = 13(n - 1), so n - 1 = 14 and n = 15. Stopping at n - 1 gives 14; 38 is the multiplier of the largest one, not the count.