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IN CASE OF 101!,
1)FIRST CONSIDER ALL MULTIPLES OF 10 EXCEPT 50. i.e. 10,20,30,40,60,70,80,90,100. HERE ZEROES =10.
2)NOW CONSIDER ALL MULTIPLES OF 5 EXCEPT 10'S ,25,50,75.(i.e. 5,15,35,45,55,65,85,95) .AND MULTIPLY THEM WITH EVEN NO. i.e. 2 . HERE ZEROES= 8.
3) NOW CONSIDER 25,50,75. AND MULTIPLY THEM WITH SOME EVEN NOS. HERE ZEROES =6
SO TOTAL TRAILING ZEROES =10+8+6=24
IN CASE OF 101!,
1)FIRST CONSIDER ALL MULTIPLES OF 10 EXCEPT 50. i.e. 10,20,30,40,60,70,80,90,100. HERE ZEROES =10.
2)NOW CONSIDER ALL MULTIPLES OF 5 EXCEPT 10'S ,25,50,75.(i.e. 5,15,35,45,55,65,85,95) .AND MULTIPLY THEM WITH EVEN NO. i.e. 2 . HERE ZEROES= 8.
3) NOW CONSIDER 25,50,75. AND MULTIPLY THEM WITH SOME EVEN NOS. HERE ZEROES =6
SO TOTAL TRAILING ZEROES =10+8+6=24
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IN EXAMPLE 13!
WE KNOW 13!=1*2*3*4*.......*13
WE OBSERVE IN BWTWEEN THERE IS 10 . HERE ZEROS=1
THEN WE OBSERVE THERE IS 5 WHICH WHEN MULTIPLIED BY AN EVEN NO. WILL GIVE A ZERO, MAY IT BE 2,4,6,8, OR 12.WE DO NOT CONSIDER 10 HERE BCOZ 10 HAS ALREADY BEEN USED.
SO IN 13! NO. OF ZEROS IS 2.