1. Total even numbers Sequence: 100, 102, ..., 998 This is an A.P. with a=100,d=2, last term 998 . n=‌
998−100
2
+1=‌
898
2
+1=449+1=450. So, 450 even numbers. 2. Even numbers divisible by 3⟶ multiples of 6 Between 100 and 998: - First multiple of 6≥100 is 102(6×17) - Last multiple of 6≤998 is 996(6×166) Count: 166−17+1=150 3. Even numbers divisible by 5⟶ multiples of 10 Between 100 and 998: - First: 100=10×10 - Last: 990=10×99 Count: 99−10+1=90
4. Even numbers divisible by both 3 and 5⟶ multiples of 30 Between 100 and 998: - First: 120=30×4 - Last: 990=30×33 Count: 33−4+1=30 5. Use inclusion-exclusion on even numbers Even numbers divisible by 3 or 5 : 150+90−30=210. 6. Not divisible by 3 or 5 450−210=240.