2009 AMC 10A Problems/Problem 19
The circumference of circle A is 200, and the circumference of circle B with radius is . Since circle B makes a complete revolution and ends up on the same point, the circumference of A must be a perfect factor of the circumference of B, therefore the quotient must be an integer.
R must then be a factor of 100, excluding 100 (because then circle B would be the same size as circle A). . Therefore 100 has factors*. Subtracting 1 from 9, so as to exclude 100, the answer is .
- The number of factors of and so on, is .