# Big circle, little circles

$$r$$, $$N$$ and $$R$$ are nonzero positive integers, and $$N$$ > 1.

$$r$$ is the radius of $$N$$ circles whose areas together are equal to the area of a single circle with radius $$R$$.

For example, if $$R = 100$$, $$r$$ could be 1, and there would be $$N=10\,000$$ circles. $$r$$ could also be 2, and there would be $$N=2500$$ circles. However, $$r$$ could not be 3, since there is no way to divide the big circle evenly into little circles with that radius.

How many different possible values of the small radius $$r$$ exist for a large radius of $$R = 90\,000$$?

×