Common Factor

A common factor is a number that can be divided into two or more other numbers without leaving a remainder. In other words, it is a number that is a factor of two or more given numbers.

Finding Common Factors

To find the common factors of two or more numbers, you can use the following methods:

1. List Method: List all the factors of each number and then find the factors that are common to all the numbers.
2. Prime Factorization Method: Find the prime factorization of each number and then identify the common prime factors. The product of these common prime factors gives the common factors of the numbers.

Example:

Find the common factors of 12 and 18.

List Method: Factors of 12 are 1, 2, 3, 4, 6, and 12. Factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors are 1, 2, 3, and 6.

Prime Factorization Method: Prime factorization of 12 = 2 x 2 x 3, and prime factorization of 18 = 2 x 3 x 3. The common prime factors are 2 and 3. Therefore, the common factors are 2 x 3 = 6.

Study Guide:

To study common factors effectively, follow these steps:

1. Understand the concept of factors and how they are related to multiplication.
2. Practice listing factors of different numbers, both manually and using mathematical techniques.
3. Learn the prime factorization method and how it helps in finding common factors.
4. Practice finding common factors of various numbers using both the list method and prime factorization method.
5. Work on real-world problems involving common factors to understand their practical applications.

Understanding common factors is important as it forms the basis for simplifying fractions, finding the greatest common factor, and solving various mathematical problems.

By mastering the concept of common factors, you will be better equipped to handle more advanced topics in mathematics.