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max n so that 10x11x12 x...x50 divisible by 10^n (HOMC 2019 JI-6)

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November 7, 2020
divisiblenumber theory

Problem Statement

What is the largest positive integer nn such that 10×11×12×...×5010 \times 11 \times 12 \times ... \times 50 is divisible by 10n10^n?
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