10. Consider the expression $1 * 2 * 3 * 4 * 5 * 6$.
Each star in the expression is to be replaced with either ' + ' or ' $x$ '.
$N$ is the largest possible value of the expression. What is the largest prime factor of $N$ ?
10. 103 Note that $6!=1 \times 2 \times 3 \times 4 \times 5 \times 6=720$. We observe that if any multiplication sign, other than the first, is replaced by an addition sign then each remaining product is at most 360. Therefore we retain each multiplication sign except the first which may be replaced by an addition sign to obtain a maximal value of 721 .
The prime factors of 721 are 7 and 103 , of which 103 is the largest.