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Q: How many numbers between 75 and 500 are divisible by 7?

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There are 232 numbers between 1 and 500 that are divisible by 3 or 5.

There are 43 natural numbers between 200 and 500 that are divisible by seven.

Exclusively, meaning not including 200 and 500, there are 149 even (divisible by two) numbers between 200 and 500.

Not sure!

29 of them.

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There are 232 numbers between 1 and 500 that are divisible by 3 or 5.

There are 43 natural numbers between 200 and 500 that are divisible by seven.

Exclusively, meaning not including 200 and 500, there are 149 even (divisible by two) numbers between 200 and 500.

Not sure!

29 of them.

55

50 of them.

There are many numbers between 500 and 1000 divisible by 3 and 9. Any number divisible by 9 is divisible by 3. How about 900?

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.

Eight of them.

There are 63 numbers 1 to 500 that are divisible by six but not by eight.

9

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