# How many zeros are at the end of the binary expansion of

## Problem 24E Chapter 4.SE

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition

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Problem 24E

How many zeros are at the end of the binary expansion of 10010!?

Step-by-Step Solution:
Step 1 of 3

Step-1:

In this problem  we need to find the number of  zeros are at the end of the binary expansion of .

Note: We know that  if we multiply a number by 2 we will see that its binary form will have a 0 increased . This means the number of 0’s at the end of a binary number is equal to the number of times 2 is the factor  of that number.

Step-2:

100 is an even number and it is clearly divisible by 2.

The number of zeros in the binary expansion of a number  n is the largest k such that divides n.

Note that ,

numbers between 1 and 100 are divisible by .

Where k

,...

Step 2 of 3

Step 3 of 3

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How many zeros are at the end of the binary expansion of

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