What is a common factor of two or more positive integers?

Conditions

• Compare two or more positive integers.
• The common factor is positive and divides each target exactly.

Reasoning, step by step

1. List all positive factors of the first number.
2. List all positive factors of the second number.
3. Identify the factors that appear in both lists.
4. These shared factors are the common factors.

Example

The factors of 12 are $\{1, 2, 3, 4, 6, 12\}$ and the factors of 42 are $\{1, 2, 3, 6, 7, 14, 21, 42\}$. The common factors are $\{1, 2, 3, 6\}$.

Common misconceptions

• Confusing a common factor with a common multiple.
• Thinking that a common factor must be the largest shared divisor.

Watch the explanation

Explore next

• What is the greatest common factor?
• How do I find the GCF of two numbers by listing factors?