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Q: What number between 200 and 300 is exactly divisible by 3 5 and by 7?

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There are 33 numbers between 200 and 300 that are divisible by three.

There are 5 multiples of 18 between 200 and 300. (An even number divisible by 9 is any number divisible by 18).

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.

The number is 115.

22,200 is a number that can be divisible by 111 and 200.

201 is one such number.

201

201

235

201 is one such.

The probability is 67/200.

These numbers between 200 and 300 are divisible by nine but not by two: 207, 225, 243, 261, 279, 297.

270.

150

231 and 285

333

How about: 270

210

There are 22 such numbers.

How about 240 or 270

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.

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There are: 210, 240 and 270.

There are two such numbers: 210 and 280.

213.