Find the number of zeroes at the end of the number 55! = 1·2·…·54·55
how many multiples of 5?
That will determine the number of zeroes (because there will be at least that many multiples of 2, as well): 13
To find the number of zeroes at the end of a factorial number like 55!, you need to determine how many times the number can be divided by 10.
A number has a trailing zero when it is multiplied by 10. Since 10 can be expressed as 2 x 5, we need to find how many times the number can be divided by 2 and 5.
For a factorial number like 55!, there are typically more 2s than 5s. So, we need to count the number of 5s.
To find the number of 5s in the factorial number 55!, we can divide 55 by 5, which gives 11. Hence, there are 11 multiples of 5 in the numbers from 1 to 55.
However, we also need to consider numbers like 25 and 50, as they have more than one factor of 5. We can divide them by 5 again to get the additional factors:
25 / 5 = 5
50 / 5 = 10
Adding these additional factors to the count, we have a total of 11 + 5 + 10 = 26 factors of 5 in the number 55!.
Therefore, the number 55! has 26 trailing zeros.