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South African Mathematics Olympiad

South Africa number theory

Problem

One of the factors of is chosen at random. What is the probability that the chosen factor is NOT a multiple of ?

(A) (B) (C) (D) (E)
Solution
There are ten factors: , , , , , , , , , . Four of them are not multiples of , viz. , , , . The probability is therefore or .
Final answer
A

Techniques

Factorization techniques