In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors C?  Choose the most appropriate option: A) 2 B) 3 C) 5 D) 6 E) 8
I like to put the numbers in prime factors so it is easier and faster to visualize.   14*n/60   If we write the factors of 14 --&gt; 2, 7, and the factors of 60 --&gt; 2, 2, 3, 5, we have   (2*7*n)/(2^2*3*5)   Simplifying   7*n/(2*3*5)   The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.   The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....   However to be less than 200 we can not add any prime number.   2*3*5 = 120   If we added the next prime factor 7, we would have C=2*3*5*7 = 840   Thus, answer 3
<result>B</result>
In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors C?