Q: What number is divisible by 2 and 5 between 100 and 200?

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150

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

There are 22 such numbers.

It is 120, 150, and 180.

12. 13, if you count 200

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.

200

100 ÷ 6 = 16 r 4 so the first whole number between 100 and 200 divisible by 6 is 6 x 17 (= 102) 200 ÷ 6 = 33 r 2 so the last whole number between 100 and 200 divisible by 6 is 6 x 33 (= 198) So the whole numbers between 100 and 200 divisible by 6 are the multiples of 6 from 17 to 33 which are: 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192 and 198.

Because the smallest such number is 210.

The numbers between 100 and 200 that are divisible by three but not by two are: 105, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 183, 189 and 195.

2 times 3 times 5 is 30 so you just have to have a number divisible by 30 so 120.

Any number that is divisible by 100 is also divisible by 20. so 100, 200, 300, 400 etc

150

14 of them

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

The number is 115.

17 of them.

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.

201 is one such number.

201

201

235

201 is one such.

The probability is 67/200.

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