2427\. Number of Common Factors

Easy

Given two positive integers `a` and `b`, return _the number of **common** factors of_ `a` _and_ `b`.

An integer `x` is a **common factor** of `a` and `b` if `x` divides both `a` and `b`.

**Example 1:**

**Input:** a = 12, b = 6

**Output:** 4

**Explanation:** The common factors of 12 and 6 are 1, 2, 3, 6.

**Example 2:**

**Input:** a = 25, b = 30

**Output:** 2

**Explanation:** The common factors of 25 and 30 are 1, 5.

**Constraints:**

*   `1 <= a, b <= 1000`