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Q: How many numbers that are divisible by 6 out of 100?

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100/6 = 16.6 recurring (that is, 16.6666...) Therefore, there are 16 numbers lower than 100 that are directly divisible by 6.

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.

There are 67 numbers between 100 and 500 divisible by 6. The first number greater than 100 divisible by 6: 100 ÷ 6 = 16 r 4 → first number divisible by 6 is 6 × 17 = 102 Last number less than 500 divisible by 6: 500 ÷ 6 = 83 r 2 → last number divisible by 6 is 6 × 83 = 498 → all multiples of 6 between 17 × 6 and 83 × 6 inclusive are the numbers between 100 and 500 that are divisible by 6. → there are 83 - 17 + 1 = 67 such numbers.

Four. 24 and its multiples.

There are two: 42 and 84.

The only one is 90.

16 of them from 6 to 96

A number that is divisible by 4 and 6 must be divisible by the LCM of 4 and 6 which is 12. 100/12 = 8.33 200/12 = 16.67 So, there are 16 numbers below 200 that are divisible by 4 and 6 and, of these, 8 are smaller than 100. That gives 16 - 8 = 8 between 100 and 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.

The numbers that are divisible by both 3 and 5 have to be a factor of 15. That leaves 15, 30, 45, 60, 75, and 90. There are 6 numbers less than 100 divisible by 3 and 5

There are 899 numbers between 100 and 1000. Every 6th number is divisible by 6. 899 divided by 6 is 149 and 5/6. The answer must be 149 or 150. The first number in that set is 102 (17 x 6). The last is 996 (166 x 6). 166 - 17 + 1 is 150. There are 150 numbers between 100 and 1000 that are divisible by 6.

There are 151 3-digit numbers that are divisible by 6.

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