There are 41 numbers between 1 and 1,000 that are divisible by 3 and 8?
100 ÷ 4 = 25 → 24 numbers between 0 and 100 exclusive are divisible by 4 100 ÷ 6 = 16 2/3 → 16 numbers between 0 and 100 are divisible by 6 lcm(4, 6) = 12 → 100 ÷ 12 = 8 1/3 → 8 numbers between 0 and 100 are divisible by 4 and 6.
8
5
All numbers that are divisible by 8 and 12 would also be divisible by 4.
There are 41 numbers between 1 and 1,000 that are divisible by 3 and 8?
100 ÷ 4 = 25 → 24 numbers between 0 and 100 exclusive are divisible by 4 100 ÷ 6 = 16 2/3 → 16 numbers between 0 and 100 are divisible by 6 lcm(4, 6) = 12 → 100 ÷ 12 = 8 1/3 → 8 numbers between 0 and 100 are divisible by 4 and 6.
8
5
12. 13, if you count 200
There are (500-100)/2 = 200 numbers divisible by 2 between 100 and 500 counting 100 but not 500. Of these (500-100)/8 = 50 are divisible by 8. So there are 150 numbers between 100 and 500 divisible by two but not by 8. By relative primeness exactly 50 out of these 150 are divisible by 3 and therefore these 50 are exactly the ones divisible by 6 but not by 8.
There are 10 such numbers between 8 and 121 that are divisible by 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110.
All numbers that are divisible by 8 and 12 would also be divisible by 4.
136, 144, 152
No number between 20 and 40 is divisible by all 4 numbers. The smallest number divisible by all 4 of those numbers is: 56
There are 5 numbers between 17 and 61 that are divisible by 8. They are 24, 32, 40, 48, and 56.
125 (including 1000)