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