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Question

The number of zeros at the end of 100! is ?


A

20

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B

22

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C

24

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D

26

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Solution

The correct option is C

24


Simplify the given factorial

Given, 100!

To get a zero at the end a number must be multiplied with 10

Therefore we need the number of times product of 2×5 occurs to find the number of zeroes.

Calculate the powers of 2 in 100!

The power of 2 is sum of 1002=50, 502=25, 252=12, 122=6, 62=3, 32=1, 12=0,

where is the Greatest integer function.

The power of 2=50+25+12+6+3+1=97

Similarly, the power of 5 is sum of 1005=20,205=4,45=0

The power of 5=20+4=24

The limiting value to decide the number of zeroes is power of 5 as it lessens than the power of 2.

Therefore, the number of 10 formed =24

there are 24 zeroes at the end of 100!, so,

Hence option C is the correct .


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