Art of Problem Solving

2025 AMC 10A Problems/Problem 17

Revision as of 12:48, 6 November 2025 by Tacos are yummy 1 (talk | contribs)

(Problem goes here)

Solution 1

The problem statement implies $N|273420$ and $N|272745.$ We want to find $N > 16$ that satisfies both of these conditions. Hence, we can just find the greatest common divisor of the two numbers. $\gcd{273420,272745}=\gcd{675,272745}=\gcd{675,45}=45,$ so the answer is $\boxed{\text{(E) }4}.$

~Tacos_are_yummy_1