Discussion
What is the highest power of 7 that divides 100! ?
Answer: C
To find the highest power of a prime p in n!, we use Legendre's formula: \(\lfloor n/p \rfloor + \lfloor n/p^2 \rfloor + ...\). Here, n=100 and p=7. The power is \(\lfloor 100/7 \rfloor + \lfloor 100/49 \rfloor = 14 + 2 = 16\). The highest power of 7 is 16.
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