Finding Common Factors

In math, it's important to understand factors. When we talk about factors, we mean numbers that multiply together to make another number. For example, 2 and 3 are factors of 6 because 2 multiplied by 3 gives 6.

Factors are numbers that you can multiply together to get another number. If 2 and 3 are multiplied to get 6, then 2 and 3 are the factors of 6. Similarly, if we consider the number 12, its factors include 1, 2, 3, 4, 6, and 12.

12: 
- 1 × 12 = 12
- 2 × 6 = 12
- 3 × 4 = 12

Multiplying each of these pairs gives the result 12. The numbers 1, 2, 3, 4, 6, and 12 are all factors of 12.

What are the common factors?

Common factors are the factors that two or more numbers have in common. In simple terms, they are the numbers that are factors of both the numbers. Let us understand this concept in more detail with some examples.

How to find common factors

Finding common factors involves a few simple steps. It's not too difficult once you understand the process. Here's how you can do it:

• List all the factors of each number.
• Identify the factors that are common in both lists.

Example 1: Finding the common factors of 8 and 12

Let's use these steps to find the common factors of 8 and 12:

Step 1: List the factors of 8.

8: 
- 1 × 8 = 8
- 2 × 4 = 8

So the factors of 8 are 1, 2, 4, and 8.

Step 2: List the factors of 12.

12: 
- 1 × 12 = 12
- 2 × 6 = 12
- 3 × 4 = 12

So the factors of 12 are 1, 2, 3, 4, 6, and 12.

Step 3: Find the common factors.

The factors 1, 2, and 4 are present in both lists. Therefore, the common factors of 8 and 12 are 1, 2, and 4.

Example 2: Finding the common factors of 15 and 25

Let's find the common factors of 15 and 25 following the same method:

Step 1: List the factors of 15.

15:
- 1 × 15 = 15
- 3 × 5 = 15

So the factors of 15 are 1, 3, 5, and 15.

Step 2: List the factors of 25.

25:
- 1 × 25 = 25
- 5 × 5 = 25

So the factors of 25 are 1, 5, and 25.

Step 3: Find the common factors.

The factors 1 and 5 appear in both lists. Thus, the common factors of 15 and 25 are 1 and 5.

Example 3: Finding the common factors of 21 and 28

Finally, let's find the common factors of 21 and 28:

Step 1: List the factors of 21.

21:
- 1 × 21 = 21
- 3 × 7 = 21

So the factors of 21 are 1, 3, 7, and 21.

Step 2: List the factors of 28.

28:
- 1 × 28 = 28
- 2 × 14 = 28
- 4 × 7 = 28

So the factors of 28 are 1, 2, 4, 7, 14, and 28.

Step 3: Find the common factors.

The common factors between the two lists are 1 and 7. Therefore, the common factors of 21 and 28 are 1 and 7.

Practice finding common factors

To understand common factors better, let's practice with some more examples:

Example: Find the common factors of 10 and 20

Step 1: List the factors of 10: 1, 2, 5, 10.

Step 2: List the factors of 20: 1, 2, 4, 5, 10, 20.

Step 3: The common factors are 1, 2, 5, and 10.

Example: Find the common factors of 18 and 24

Step 1: List the factors of 18: 1, 2, 3, 6, 9, 18.

Step 2: List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

Step 3: The common factors are 1, 2, 3, and 6.

Example: Find the common factors of 9 and 27

Step 1: List the factors of 9: 1, 3, 9.

Step 2: List the factors of 27: 1, 3, 9, 27.

Step 3: The common factors are 1, 3, and 9.

Conclusion

Finding common factors is a basic math skill. It starts with understanding what factors are and then identifying which factors two numbers share. Practicing with different numbers helps strengthen this skill. Remember, listing all the factors is important to ensure you find all the common factors. Keep practicing, and soon, finding common factors will become second nature to you!

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