Question
10000!=(100!)K∗P, where K and P are integers. Then what is the maximum value of K?
Answer: Option A
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A
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option (A)
The key here are the prime numbers. K should be selected in such a way that it will depict the value of the highest power of the largest prime number before 100 which is a factor of 10000!. The largest prime number below 100 is 97 and the highest power of 97 in 10000! is 104.
→ But the highest power of 297 in 10000! is 103
This step needs to kept in mind
hence 103 is the highest power of 100! in 10000!
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