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Author: BaffinLee

101-200/172. Factorial Trailing Zeroes.md

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+# 172. Factorial Trailing Zeroes
+
+- Difficulty: Easy.
+- Related Topics: Math.
+- Similar Questions: Number of Digit One, Preimage Size of Factorial Zeroes Function.
+
+## Problem
+
+Given an integer *n*, return the number of trailing zeroes in *n*!.
+
+**Example 1:**
+
+```
+Input: 3
+Output: 0
+Explanation: 3! = 6, no trailing zero.
+```
+
+**Example 2:**
+
+```
+Input: 5
+Output: 1
+Explanation: 5! = 120, one trailing zero.
+```
+
+**Note: **Your solution should be in logarithmic time complexity.
+
+## Solution
+
+```javascript
+/**
+ * @param {number} n
+ * @return {number}
+ */
+var trailingZeroes = function(n) {
+  if (n === 0) return 0;
+  return Math.floor(n / 5) + trailingZeroes(Math.floor(n / 5));
+};
+```
+
+**Explain:**
+
+nope.
+
+**Complexity:**
+
+* Time complexity : O(log(n)).
+* Space complexity : O(1).