Find the number of zeros in 101!A] 27 B] 21 C] 12 D] 24Options :ABCD
Question
Find the number of zeros in 101!
- A] 27
- B] 21
- C] 12
- D] 24
Options : A B C D
Solution
The number of zeros in a factorial can be found by counting the number of times 10 is a factor in the numbers from 1 to the number. 10 is a product of 2 and 5. Since there are usually more 2s than 5s, we just need to count the number of 5s.
Here are the steps to find the number of zeros in 101!:
-
Divide 101 by 5, you get 20. This is the number of numbers less than 101 that are divisible by 5.
-
Divide 101 by 25 (5^2), you get 4. This is the number of numbers less than 101 that are divisible by 25 (and thus contribute an extra factor of 5).
-
Divide 101 by 125 (5^3), you get 0. This is the number of numbers less than 101 that are divisible by 125 (and thus contribute an extra factor of 5).
-
Add up these counts: 20 + 4 + 0 = 24.
So, the number of zeros at the end of 101! is 24. Therefore, the answer is D] 24.
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