Trailing Zeros
How many zeros does 50! have at the end?
Age
11 to 14
Challenge level
Problem
The symbol $50!$ represents the product of all the whole numbers from $1$ to $50$ inclusive; that is, $50!=1 \times 2 \times 3 \times \dots \times 49 \times 50$. If I were to calculate the actual value, how many zeros would the answer have at the end?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 12
$\times$10 adds a zero (or $\times$2$\times$5)
If a number ends in zero, it must be a multiple of 10
So count how many times 10 or 2$\times5$ appears
Image
10 multiples of 5 plus 2 more for 50 and 25 = 12