Detailed Explanation 1. How do we get a zero? A trailing zero is… — 𝗕𝘁𝗲𝗰𝗵 & 𝗚𝗮𝘁𝗲 𝗦𝘁𝘂𝗱𝘆 𝗺𝗮𝘁𝗲𝗿𝗶𝗮𝗹 — TG.ME

Detailed Explanation 1. How do we get a zero? A trailing zero is created every time you multiply a 2 and a 5 (because 2 × 5 = 10). In 100! (which is 100 × 99 × 98 × ... × 1), there are plenty of even numbers, meaning we have more than enough 2s. Therefore, the number of trailing zeros is determined entirely by how many 5s are hiding inside the numbers from 1 to 100. 2. Counting the 5s (Step 1): First, we count every number that is a multiple of 5 (5, 10, 15, 20... up to 100). Formula: 100 ÷ 5 = 20 So, there are 20 numbers that give us at least one 5. 3. The Trap (Why the answer isn't 20): Some numbers contain more than one 5. Take the number 25, for example. 25 is 5 × 5 (it has two 5s). The numbers 25, 50, 75, and 100 all have an "extra" 5 hiding in them. Our first step only counted one of them! 4. Counting the extra 5s (Step 2): To count those extra 5s, we divide 100 by 25 (which is 5 squared). Formula: 100 ÷ 25 = 4 So, there are 4 extra 5s. (Note: We don't need to check for 125 (5 cubed) because 125 is bigger than 100). 5. Final Total: Add them together: 20 (from the multiples of 5) + 4 (from the multiples of 25) = 24 total 5s. Because there are exactly 24 fives (and plenty of twos to pair them with), there will be exactly 24 trailing zeros at the end of 100!.