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Number Theory Level 2

A teacher wanted to equally distribute 2017 candies to her class of no more than 50 students, but she found out that after distributing the candies evenly, there is a total of 22 candies remaining.

What is the total number of students in this class?


The answer is 35.

Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

SInce 2017 − 22 = 1995 2017 - 22 = 1995 candies are distributed evenly among n ≤ 50 n \le 50 students, we also require n n to be a factor of 1995 1995 greater than 22 22 , (for otherwise the teacher would be able to continue evenly distributing some of the remaining 22 22 candies).

Now as 1995 = 3 × 5 × 7 × 19 1995 = 3 \times 5 \times 7 \times 19 , the only factor between 22 22 and 50 50 , and hence the desired value for n n , is 5 × 7 = 35 5 \times 7 = \boxed{35} .

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