Question

Number of zeros at the end of 26!is,​

Answer 1

Answer:

6

Step-by-step explanation:

$26! = 26 * 25 * 24 * ... * 3 * 2 * 1$

In this expression, each occurrence of '10' accounts for a trailing zero. Now, 10 is made up of 2's and 5's. Again, the number of multiples of 5 is less than that of 2. So, 5 is limiting the number of zeroes. Number of multiples of 5 less than 26 = (26/5) = 5. But, 25 has an extra 5. So, total number of times 5 occurs as a factor in 26! is (5+1) = 6. Hence, the number of trailing zeroes in 26! is 6. (Ans)