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Largest power of 10 dividing n! (count factors of 5)

The same question, asked 2 times: CDS 1 2018*, CDS 1 2023. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2018

    83
    What is the largest power of 10 that divides the product 1×2×3×4…×23×24×251 \times 2 \times 3 \times 4 \ldots \times 23 \times 24 \times 25 ?

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  2. Question 2

    CDS 1 2023

    2
    What is the largest power of 10 that divides the product 29×28×27×…2×129 \times 28 \times 27 \times \ldots 2 \times 1?

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