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jmc

number theory intermediate

Problem

Divide the product of the first five positive composite integers by the product of the next five composite integers. Express your answer as a common fraction.
Solution
The first ten positive composite integers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. The desired quotient is . After cancellation, we get .
Final answer
\frac{1}{42}