Common Factor

A common factor of two or more numbers is a number that divides each of the given numbers without leaving a remainder.

Finding Common Factors

To find the common factors of two numbers, you can list all the factors of each number and then identify the factors that appear in both lists. Another method is to use prime factorization. Once you have the prime factorization of the given numbers, you can identify the common prime factors and then multiply them together to find the common factors.

Example

Find the common factors of 24 and 36.

1. Find the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
2. Find the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12.

Study Guide

Here are the key points to remember about common factors:

1. A common factor of two or more numbers is a number that divides each of the given numbers without leaving a remainder.
2. To find the common factors of two numbers, you can list all the factors of each number and then identify the factors that appear in both lists.
3. Another method for finding common factors is to use prime factorization.
4. Common factors are important in simplifying fractions and finding the greatest common factor (GCF) of two numbers.

Practice finding common factors by working through example problems and using both the listing method and prime factorization method.

Understanding common factors is important for various topics in mathematics, including simplifying fractions, finding the greatest common factor, and solving equations. Make sure to practice and review this concept to strengthen your understanding.