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Number theory Difficulty 3.0 AMC 10/12 Prove it Canada

The number $5\,41G\,507\,2H6$ is divisible by 72. If $G$ and $H$ each represent a single digit, what pairs of values of $G$ and $H$ are possible? Explain how you obtained your answer.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.