Common Factor — Definition, Formula & Examples
A common factor is a whole number that divides evenly into two or more numbers. For example, 4 is a common factor of 12 and 20 because it divides both without a remainder.
Given two or more integers, a common factor is any positive integer such that divides each of those integers exactly, meaning each division produces a remainder of zero.
How It Works
To find the common factors of two numbers, list all the factors of each number separately. Then look for the numbers that appear in both lists. Every pair of whole numbers shares at least one common factor: the number 1.
Worked Example
Problem: Find all the common factors of 18 and 24.
Step 1: List the factors of 18.
Step 2: List the factors of 24.
Step 3: Pick out the numbers that appear in both lists.
Answer: The common factors of 18 and 24 are 1, 2, 3, and 6.
Why It Matters
Finding common factors is the first step toward simplifying fractions. When you divide the numerator and denominator by a common factor, the fraction gets smaller and easier to work with. This skill also prepares you for finding the greatest common factor, which you will use throughout pre-algebra and algebra.
Common Mistakes
Mistake: Forgetting that 1 is always a common factor of any two whole numbers.
Correction: Every whole number is divisible by 1, so 1 will always appear in both factor lists.