If 26!=n8^{k}, where k and n are positive integers, then what is the <strong>MAXIMUM</strong> value of k?
- A. 6
- B. 7 ✓
- C. 8
- D. 9
Correct Answer: B. 7
Explanation
The maximum power of 2 dividing 26! is given by Legendre's formula: \lfloor\frac{26}{2}\rfloor + \lfloor\frac{26}{4}\rfloor + \lfloor\frac{26}{8}\rfloor + \lfloor\frac{26}{16}\rfloor = 13 + 6 + 3 + 1 = 23. Since 8 = 2^3, the maximum power of 8 dividing 26! is \lfloor\frac{23}{3}\rfloor = 7.
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