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UKMT Senior Mathematical Challenge, 2023

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

The greatest power of $7$ which is a factor of $50!$ is $7^k$ ( $n! = 1 \times 2 \times 3 \times 4 \times \ldots \times (n-1) \times n$ ). What is $k$ ?

(A) $4$ (B) $5$ (C) $6$ (D) $7$ (E) $8$

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