[Saikrish Kailash]

Answer is 1170.

Zero in end digits comes when we multiply 5 with even numbers ...

1! = 1  = 1

2! = 1*2 = 1

3! = 1*2*3 = 6

4! = 1*2*3*4 = 24

5! = 1*2*3*4*5 = 120

120 has one zero and n has one five..

same lines if we move forward next additional zero will come when we reach 10!

10! will have two end digit zero.

So we need to find n which gives us 290 end zero.

check with 100 ! - we will get 24 5's & hence 24 zeros ...which is less than expected 290 zeros..

move with 1000!

1000 has 249 5's

so we move forward say 1200 has 298 5's and hence 298 zero.

1150 has 286 5's and hence 286 zero.

On same lines if we move we will get 1170.

 

 

 

 

[Saikrish Kailash]

Equivalence Relation guarantees Partition derivation but reverse is not true.

[Saikrish Kailash]

[Saikrish Kailash]

if a ~ a mod m then a-a is divided y m

if a ~ c mod m then a-c is divided y m so -(c-a) is divided y m

if a ~ c mod m , c ~ d mod m then a-c divided y m and c-d divided y m .. so a-c + c-d divided y m .. then a-d divided y m so a ~ d mod m

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