tough number properties

[ashish1354]

How many integers less than 1000 have no factors (other than 1) in common with 1000?

my question is whether we need to consider integers starting from 0 till 999

& if we do do we need to include 0??

[Morgoth]

I guess you have to consider 0. Since 0 is a factor of no number and multiple of every number.

But on GMAT you generally get things like positive integers or positive factors in the question stem itself. So, you dont have to consider 0 then.

0 is an integer neither positive nor negative.

[Ian Stewart]

How many integers less than 1000 have no factors (other than 1) in common with 1000?

my question is whether we need to consider integers starting from 0 till 999

& if we do do we need to include 0??

If the question simply says 'How many integers less than 1000', you'd even need to consider negative numbers, so the answer would be 'an infinite number'. You won't see a question like that on the GMAT- if you saw such a question, it would say 'positive integers', in which case you would not, of course, consider zero, since zero is not positive.

[4meonly]

What is the answer?
400?

[pre-gmat]

Yeah I guess answer should be 400.

here's my reasoning...

1000 has 2,5 as prime factors.

so first eliminate all even numbers which leaves 500 odd integers and now out of 500 eliminate any number divisible by 5 which is 100 and therefore leaves us with 400.
We haev already covered the case of 2 and 5 together being factor.


Let me know the OA.