Gcf of 28 and 24 distributive property – The distributive property of multiplication over addition provides a powerful tool for understanding the relationship between numbers. In this exploration, we delve into the distributive property to uncover the greatest common factor (GCF) of 28 and 24, revealing its practical applications in various fields.
The concept of GCF, often referred to as the greatest common divisor, lies at the heart of number theory. By employing the distributive property, we can systematically determine the largest factor that divides both numbers without leaving a remainder, offering valuable insights into their divisibility and common characteristics.
Distributive Property of Multiplication over Addition: Gcf Of 28 And 24 Distributive Property
The distributive property of multiplication over addition states that the product of a number and a sum is equal to the sum of the products of the number and each of the addends. In other words, for any number a, and any numbers band c, we have:
a( b+ c) = ab+ ac
This property can be illustrated with the following examples:
- 3(2 + 4) = 3(2) + 3(4) = 6 + 12 = 18
- -5(x + y) = -5(x) + (-5)(y) = -5x – 5y
Greatest Common Factor (GCF), Gcf of 28 and 24 distributive property
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. For example, the GCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.
The distributive property can be used to find the GCF of two numbers. To do this, we first factor each number into its prime factors. Then, we identify the prime factors that are common to both numbers. The product of these common prime factors is the GCF of the two numbers.
GCF of 28 and 24
To find the GCF of 28 and 24 using the distributive property, we first factor each number into its prime factors:
- 28 = 2 2– 7
- 24 = 2 3– 3
The common prime factors of 28 and 24 are 2 and 2. Therefore, the GCF of 28 and 24 is:
GCF(28, 24) = 2 – 2 = 4
The following table summarizes the steps involved in finding the GCF of 28 and 24 using the distributive property:
| Step | Description |
|---|---|
| 1 | Factor each number into its prime factors. |
| 2 | Identify the common prime factors of the two numbers. |
| 3 | Multiply the common prime factors together. |
| 4 | The product is the GCF of the two numbers. |
Applications of GCF
The GCF has many applications in real-world situations. For example, it is used to:
- Simplify fractions
- Find the least common multiple (LCM) of two numbers
- Solve systems of linear equations
- Design geometric shapes
Expert Answers
What is the distributive property?
The distributive property states that for any number a, b, and c, a(b + c) = ab + ac.
What is the GCF of two numbers?
The GCF of two numbers is the largest number that divides both numbers without leaving a remainder.
How do you find the GCF of two numbers using the distributive property?
To find the GCF of two numbers using the distributive property, factor each number into its prime factors and then multiply the common prime factors together.
