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    OlympiadMediumNumber Theory7–9

    What is the smallest positive integer n for which the product 1 \times 2 \times \cdots \times n is divisible by 1000?

    Qual é o menor inteiro positivo n para o qual o produto 1 \times 2 \times \cdots \times n é divisível por 1000?

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    Solution

    Step 1 of 3

    1. 1.1000 = 2^3 \times 5^3, and factors of 5 are far scarcer than factors of 2.