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UKMT Senior Mathematical Challenge, 2020

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

The number $16! \div 2^k$ is an odd integer. Note that $n! = 1 \times 2 \times 3 \times \cdots \times (n-1) \times n$ . What is the value of $k$ ?

(A) $9$ (B) $11$ (C) $13$ (D) $15$ (E) $17$

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