(Q). Find the highest power of 20 in 10! × 20! × 30! × 40! × 50! × 60! × 70! × 80! × 90! × 100! × 110! × 120!.
Solution:-
20 = 2² × 5
for 10! ⇒
Since out of given factorial numbers 10! is least & in 10! highest power of 5 (i.e. 2) is less than highest power of 2² (i.e. 4)
Hence as the value of factorial number ↑, highest power of 2 or 2² will always be greater than highest power of 5.
So for maximum power of 20 we have to find only max power of 5 in every factorial & add all of them.⇒