Method of Common Factors The Method of Common Factors is a systematic approach used to determine the greatest common factor (GCF) and common factors of...
Method of Common Factors
The Method of Common Factors is a systematic approach used to determine the greatest common factor (GCF) and common factors of two or more numbers.
Step 1: Arrange the numbers in descending order. This allows us to identify the greatest common factor by focusing on the largest numbers first.
Step 2: Identify the factors of each number. This involves finding all the whole numbers that evenly divide the original number.
Step 3: Write down the factors of each number. This creates a list of all the different factors we have found.
Step 4: Find the GCF. The GCF is the largest number that appears in the list of factors.
Step 5: Find the common factors. The common factors of two numbers are the numbers that appear in both their lists of factors.
Example:
Let's say we have the following two numbers: 12 and 18.
Step 1: Arrange the numbers in descending order:
18 > 12
Step 2: Identify the factors of each number:
12 factors: 1, 2, 3, 4, 6, 12
18 factors: 1, 2, 3, 6, 9, 18
Step 3: Write down the factors of each number:
| Number | Factors |
|---|---|
| 12 | 1, 2, 3, 4, 6, 12 |
| 18 | 1, 2, 3, 6, 9, 18 |
Step 4: Find the GCF:
The GCF of 12 and 18 is 6.
Step 5: Find the common factors:
The common factors of 12 and 18 are 1, 2, 3, and 6