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UKMT Senior Kangaroo, 2016

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Consider the expression $1 * 2 * 3 * 4 * 5 * 6$ . Each star in the expression is to be replaced with either '+' or $'\times'.$ $N$ is the largest possible value of the expression. What is the largest prime factor of $N$ ?

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