Factoring Fundamentals
Greatest Common Factor (GCF)
The greatest common factor, or GCF, is the largest factor shared by two or more numbers. It tells you the biggest number you can divide out of every term.
What is the greatest common factor?
Several numbers can be common factors, but only the largest one is the GCF. For 12 and 18, both 2 and 3 are common factors, but 6 is greater than both.
How to find the GCF
- List the factors of each number.
- Identify the factors that appear in every list.
- Choose the largest shared factor.
Worked example
Find GCF(12, 18)
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Shared factors: 1, 2, 3, 6
The largest shared factor is 6, so GCF(12, 18) = 6.
Common mistakes
- Stopping at the first common factor instead of the greatest one.
- Choosing a number that does not divide every term.
- Forgetting that the GCF can be 1.
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