Question

Find the highest power of 21 in (100!)

Answer 1

highest power of 21 in (100!) is 16

Prime factors of 21 are 3 and 7

7 > 3

Hence power of 7 will decide power of 3

Power of 7 in 100! can be find as:

[ 100/7¹]  + [100/7²]  + [100/7³] + ...

[] represent greatest integer function

[ 100/7]  + [100/49]  + [100/343] + ...

= 14 + 2 + 0 + 0 ...

= 16

Hence highest power of 7 in 100! will be 16

so highest power of 21 in (100!) is 16