How many trailing zeros does 50! have? e.g.301000 has three trailing z

Question

How many trailing zeros does 50! have? e.g.301000 has three trailing zeros

A) 5
B) 6
C) 10
D) 12
E) 13

GMATinsight · Answer

Please find below the video solution with basic concept of prime factorization of any factorial.

https://www.youtube.com/watch?v=XabmxMN3CHU

Answer: Option D

Archit3110 · Answer

We can solve 50/5+50/25 : 10+2:12
IMO D

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EgmatQuantExpert · Answer

Check this article for details:  Variations in Factorial Manipulation

Solution

To find  
We need to determine
 • The number of trailing zeros of 50!

Approach and Working out  
Theoretically, the number of trailing zeros of any factorial is determined by the highest power of 10 in that factorial.
 • As 10 = 2 x 5, we need to determine the number of instances of 2 and 5, and check how many pairs of 2 x 5 can be formed
• However, in a factorial value the instances of 5 are always less than the instances of 2. Hence, calculating the instances of 5 will be sufficient.

Number of 5s in 50! =  \frac{50}{5} + \frac{50}{5^2}  = 10 + 2 = 12

Thus, option D is the correct answer.

Correct Answer: Option D

Abhishek009 · Answer

50/5 = 10
10/5 = 2

So , Total No of trailing 0's will be 12 , Answer must be (D)

fauji · Answer

To find the number of trailing zeros we need to check power of 5 when divided by 50!

So 50!/5 = 10+2 = 12

Option D

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bumpbot · Answer

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How many trailing zeros does 50! have? e.g.301000 has three trailing z

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How many trailing zeros does 50! have? e.g.301000 has three trailing z

Prep Toolkit

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