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Largest power of a number dividing a factorial

This type of question, asked 4 times: 8 Apr 2023, 2 Apr 2025, 21 Jan 2026 S2, 24 Jan 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    8 Apr 2023

    84
    The largest natural number nn such that 3n3^{n} divides 66! Is

  2. Question 2

    2 Apr 2025

    51
    The largest n∈Nn \in N such that 3n3^{n} divides 50 ! is:

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  3. Question 3

    21 Jan 2026 S2

    70
    The largest n∈Nn \in N, for which 7n7^{n} divides 101!, is :

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  4. Question 4

    24 Jan 2026 S2

    60
    The largest value of n , for which 40n40^{n} divides 60 !, is

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