write 28+24 as a product of two factors using gcf

2 min read 19-10-2024

write 28+24 as a product of two factors using gcf

Factoring expressions is a fundamental concept in algebra that allows us to break down complex mathematical problems into simpler components. In this article, we will explore how to write the expression (28 + 24) as a product of two factors, utilizing the greatest common factor (GCF). This method is not only effective but also helps deepen our understanding of number relationships.

Understanding the GCF

What is the GCF?

The GCF, or greatest common factor, is the largest integer that divides two or more numbers without leaving a remainder. Finding the GCF is a crucial step in simplifying expressions and is particularly useful in factoring.

How to Find the GCF

To find the GCF of two numbers, you can follow these steps:

List the Factors: Write down the factors of each number.
Identify Common Factors: Determine the factors that are common to both lists.
Select the Greatest: Choose the largest number from the common factors.

Let’s apply this to our numbers: (28) and (24).

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Common Factors of 28 and 24

From the lists above, the common factors are: 1, 2, and 4. The greatest of these is 4.

Factoring 28 + 24 Using the GCF

Step-by-Step Process

Now that we have identified the GCF as (4), we can use it to factor the expression (28 + 24).

Factor out the GCF: [ 28 + 24 = 4 \times (7 + 6) ]
Rewrite the Expression: We can simplify the expression inside the parentheses: [ 7 + 6 = 13 ] Thus, we can rewrite the original expression: [ 28 + 24 = 4 \times 13 ]

Conclusion

Therefore, we can express (28 + 24) as a product of two factors: [ 28 + 24 = 4 \times 13 ]

Practical Examples

Understanding how to use the GCF to factor can be beneficial in various mathematical applications. For instance, when simplifying algebraic expressions or solving equations, recognizing factors can lead to more straightforward solutions.

Real-World Application

In real-world scenarios, this method can also be applied to partition resources or materials evenly. For example, if you have (28) apples and (24) oranges, you can group them into sets of (4) fruits each:

You could have (7) sets of apples ((28 / 4 = 7))
You could also have (6) sets of oranges ((24 / 4 = 6))

This kind of grouping helps in effective distribution, ensuring each set has equal amounts of different fruits.

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Key Takeaways

Finding the GCF: A useful technique for simplifying and factoring expressions.
Factoring Process: Break down expressions into simpler forms for easier calculations.
Practical Use: This method has real-world applications in resource distribution and organization.

By mastering the art of factoring using the GCF, you can enhance your math skills and approach problems with greater confidence and clarity.