Math, asked by aishwaryasrikar, 4 months ago

Find the highest power of 21 in (100!)

Answers

Answered by amitnrw

3

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

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