What is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1? Choose the correct answer
A) 100	B) 200	C) 300	D) 400	E) 500
Since 1000=2^3*5^3 then a number can not have 2 and/or 5 as a factor.   The odd numbers do not have 2 as a factor and there are 500 odd numbers from 1 to 1000.   We then need to eliminate the 100 numbers that end with 5, that is 5, 15, 25,...,995.   There are a total of 500 - 100= 
<gadget id="calculator">500 - 100</gadget>
<output>400</output>
400 such numbers between 1 and 1000.   The answer is 400.
<result>D</result>
What is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1?