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    OlympiadHardNumber Theory5–6

    The product 1×2×3×⋯×121 \times 2 \times 3 \times \cdots \times 12 is written out in full. How many zeros does it end with?

    O produto 1×2×3×⋯×121 \times 2 \times 3 \times \cdots \times 12 é escrito por extenso. Em quantos zeros termina?

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    Solution

    Step 1 of 3

    1. 1.Each final zero comes from a factor 10=2×510 = 2 \times 5, and there are far more factors 22 than factors 55.