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(Q). If highest power of 8 in N! is 19. Then find the highest power of 8 in (N+1)!.
Solution:-
 

Highest power of 8 in N! = 19
∴ highest power of 2 in N! = 57, 58 or 59
now we are to find such value of N
To find such N ⇒ 

341683115730157635756622222221784166222222222222222324311310Hence N = 62! or 63!∴ when N = 62! then N + 1 = 63!2222226331157310H = 57Hence max power of 2 in 63! = 57∴ max power of 8 in 63! = = 192222226432168421when N = 63! then N+1 = 64!20Hence max power of 8 in 64! = = 21& if max power of 2 in N! is 58 or 59 then No such numberexists which has max power of 2 as 58 or 59 in its factorialH = 63Hence final answer = highest power of 8 in (N+1)! = 21 Answer