Art of Problem Solving

2025 AMC 10A Problems/Problem 17: Difference between revisions

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==Solution 1==
==Solution 1==
The problem statement implies <imath>N|273420</imath> and <imath>N|272745.</imath> We want to find <imath>N > 16</imath> that satisfies both of these conditions. Hence, we can just find the greatest common divisor of the two numbers. <imath>\gcd{273420,272745}=\gcd{675,272745}=\gcd{675,45}=45,</imath> so the answer is <imath>\boxed{\text{(E) }4}.</imath>
The problem statement implies <imath>N|273420</imath> and <imath>N|272745.</imath> We want to find <imath>N > 16</imath> that satisfies both of these conditions. Hence, we can just find the greatest common divisor of the two numbers. <imath>\gcd(273420,272745)=\gcd(675,272745)=\gcd(675,45)=45,</imath> so the answer is <imath>\boxed{\text{(E) }4}.</imath>


~Tacos_are_yummy_1
~Tacos_are_yummy_1

Revision as of 12:48, 6 November 2025

(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