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Largest n such that 10^n divides a given product of powers

The same question, asked 2 times: CDS 1 2019*, CDS 2 2019. Every wording below, oldest first.

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  1. Question 1

    CDS 1 2019

    86
    If 10n10^n divides 623×759×10526^{23} \times 75^9 \times 105^2, then what is the largest value of nn ?

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  2. Question 2

    CDS 2 2019

    2
    What is the largest value of nn such that 10n10^n divides the product 25×33×48×53×67×76×812×99×106×1512×2014×2211×25152^5 \times 3^3 \times 4^8 \times 5^3 \times 6^7 \times 7^6 \times 8^{12} \times 9^9 \times 10^6 \times 15^{12} \times 20^{14} \times 22^{11} \times 25^{15} ?

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