Question
10000!=(100!)K∗P, where K and P are integers. Then what is the maximum value of K?
Answer: Option A
:
A
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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:
A
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!
Was this answer helpful ?
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