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jmc

prealgebra senior

Problem

A number is chosen at random from the set of consecutive natural numbers . What is the probability that the number chosen is a factor of ? Express your answer as a common fraction.
Solution
The number has prime factorization . A factor of 24 must have between zero and three 2's in its prime factorization, and between zero and one 3's in its prime factorization. Therefore, 24 has factors, and the probability that a number randomly chosen from the given set is a factor of 24 is .
Final answer
\frac{1}{3}