What is the total number of positive integers that are less than 800 and that have no positive factor in common with 800 other than 1? Choose the correct choice from the following answers:
A) 200 B) 320 C) 480 D) 500 E) 600
Since 800=2^5*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 400 odd numbers from 1 to 800.   We then need to eliminate the 80 numbers that end with 5, that is 5, 15, 25,...,795.   There are a total of 400 - 80= 
<gadget id="calculator">400 - 80</gadget>
<output>320</output>
320 such numbers between 1 and 800.   The answer is 320.
<result>B</result>
What is the total number of positive integers that are less than 800 and that have no positive factor in common with 800 other than 1?