What is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1?  Choose the correct choice from the following answers.
A) 60  B) 70  C) 80  D) 90  E) 100
Since 200=2^3*5^2 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 100 odd numbers from 1 to 200.   We then need to eliminate the 20 numbers that end with 5, that is 5, 15, 25,...,195.   There are a total of 100 - 20= 
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
80 such numbers between 1 and 200.   The answer is 80.
<result>C</result>
What is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1?