wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

10000!=(100!)K∗P, where K and P are integers. Then what is the maximum value of K?

A
103
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
104
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
105
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
102
No worries! We‘ve got your back. Try BYJU‘S free classes today!
E
100
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 103

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!


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon