Question

The sum of 9 distinct positive integers is 2009. Find the maximum possible value of the greatest common divisor of these 9 numbers.

Answer 1

49

Explanation:

The greatest common divisor of the addends must also be a divisor of 2009. That number can be factored as ...

2009 = 1×2009 = 7×287 = 41×49

The largest possible factor such that the other factor can be a sum of 9 positive integers is 49.

The maximum value of the GCD is 49.