What is the maximum value of n such that 5^n divides (30! +35 !), where n is a natural number?

Step-by-step solution

aligned & 30!+35!=30!+35.34 .33 .32 .31 .30! & 30!(1+35.34 .33 .32 .31) & 1+35!.34 .33 .32 .31 is not divisible by 5 aligned So, maximum value of n such that 5^n divides 30 ! aligned & = [ 30 5 ]+ [ 30 5^2 ]+ [ 30 5^3 ]+ & =6+1+0+0 =7 aligned