Latest self Aptitude Question SOLUTION: 1000! contains how many trailing zeros? Could anybody explain how to find that in any simple way??

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(#M40008961) SELF question 0's Keep an EYE

1000! contains how many trailing zeros? Could anybody explain how to find that in any simple way??

Vignesh (12 years ago)

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Pargat Pal Singh  (12 years ago)

1000/5 +1000/25 +1000/125 +1000/625= 200+40+8+1= 249

249 trailing zeros in 1000 !.

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Vignesh  (12 years ago)

Found Solution : 249 trailing zeros in 1000!

Explanation : (May be clear to someone)

In factorial we get Zero only when we get multiplied by 5 or multiples of 5.
Therefore,
From 1 to 1000, multiples of 5 = 1000/5 = 200 times (5,10,15,20,.......,995,1000)
From 1 to 1000, multiples of 5^2 = 1000/25 = 40 times (25,50,75,......,975,1000)
From 1 to 1000, multiples of 5^3 = 1000/125 = 8 times (125,250,....,875,1000)
From 1 to 1000, multiples of 5^4 = 1000/625 = 1 time only (625 only)

After that we not able to find multiples of 5. Because 5^5 = 3125(exceeds 1000)

Now, we add all = 200+40+8+1 = 249 trailing zeros in 1000!

:-)

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Ashu  (12 years ago)

249 trailing zeros are there.

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Pargat Pal Singh  (12 years ago)

1000/5 +1000/25 +1000/125 = 200+40+8= 248

248 trailing zeros in 1000 !.

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