What is the number of zeroes at the right end in the integer value of

Question

What is the number of zeroes at the right end in the integer value of 200!/100! ?

A. 0
B. 20
C. 24
D. 25
E. Greater than 25

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Dereno · Accepted Answer

We need to find : number of zeroes at the right end in the integer value of 200!/100!

200! can be rewritten as  1*2*3*4*.......*98*99*100 * 101*102*103*............*198*199*200.

The bolded part can be represented as 100! =  1*2*3*4*.......*98*99*100.

So, the entire equation becomes (100! * 101*102*103*............*198*199*200)/ 100!

= 101*102*103*............*198*199*200

We need to find the number of zeroes for 101*102*103*............*198*199*200

= Number of Zeroes for 200! - Number of Zeroes for 100!

200! On successive division by 5, yields 40+8+1 = 49.

Similarly, 100! On successive division by 5 yields 20+4 = 24.

= 49 - 24

=  25

Option D

ExpertsGlobal5 · Answer

Explanation:

https://www.youtube.com/watch?v=ca_u64M9JNU

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