What is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1? Choices.
A) 50
B) 100
C) 200
D) 300
E) 400
Since 500=2^2*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 250 odd numbers from 1 to 500.   We then need to eliminate the 50 numbers that end with 5, that is 5, 15, 25,...,495.   There are a total of 250 - 50= 
<gadget id="calculator">250 - 50</gadget>
<output>200</output>
200 such numbers between 1 and 500.   The answer is 200.
<result>C</result>
What is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1?