How many 3-digit natural numbers are divisible by 7 but not divisible by 3?

3-digit numbers run from 100 to 999. Multiples of 7 between 100 and 999: Smallest multiple ≥100 is 7×15 = 105 (since 7×14 = 98 < 100). Largest multiple ≤999 is 7×142 = 994. Count of multiples of 7 = 142 − 15 + 1 = 128. Numbers divisible by both 7 and 3 are multiples of LCM(7,3) = 21. Multiples of 21 between 100 and 999: Smallest multiple ≥100 is 21×5 = 105. Largest multiple ≤999 is 21×47 = 987. Count = 47 − 5 + 1 = 43. So numbers divisible by 7 but not by 3 = 128 − 43 = 85.