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1-1000, that's a thousand numbers. How many of them are not multiples of 2, 3 or 5? watch

1. 1-1000, that's a thousand numbers. How many of them are not multiples of 2, 3 or 5?
2. Share your thoughts with us.
3. (Original post by Mr M)
Every even number is a multiple of 2, so 500.
=>Every 3 multiples of 2, there are 2 multiples of 3, but one is a cross over (multiple of 6) so added to the 500 multiples of 2 there are 250 multiples of 3.
2*5 = 10 and 3*5 = 15........
=> Every 3 multiples of 5, one is also a multiple of 2, and the other a multiple of 3. Hence if there are 200 multiples of 5 from 1 to 1000.

So the sum of all these are 500+ 250 +200 = 950

Now I need to subtract the numbers counted more than once?
4. I think there's a way of doing this question using modular arithmetic.

Edit: Yes, you subtract the ones that come up more than once.
5. It's easier to work out how many there are in 1-30 and then multiplying by 33 to give the number that exist between 1-990 then add the last few.

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Updated: March 5, 2013
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