# Numerator sixty

$\frac{60}{61},\ \frac{60}{67},\ \frac{60}{71},\ \ldots$

How many reduced positive fractions less than 1 are there with the numerator equal to 60 and the denominators less than 10,000?


Clarification:

• The fraction $$\frac{60}{122}$$ does not count because it can be reduced to $$\frac{30}{61}$$.
• The fractions $$\frac{60}3$$ and $$\frac{60}{60}$$ do not count because they are not less than 1.
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