Art of Problem Solving

Common divisor: Difference between revisions

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* [[Euclidean algorithm]]
* [[Euclidean algorithm]]
* [[Common multiple]]
* [[Common multiple]]
 
* [[Greatest common divisor]]
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Latest revision as of 09:14, 14 October 2025

A common divisor of two or more integers is a divisor of all those integers. For any set of positive integers, there is a greatest common divisor.

Problems

Introductory

  • Find the greatest common divisor of 12, 99, and 111.

Intermediate

  • Prove that the greatest common divisor of two numbers times the least common multiple of those two numbers is equal to the product of the two numbers.

See also