The greatest common factor (GCF) of 18 and 24 is 6. This means that 6 is the largest number that is a factor of both 18 and 24. To understand GCF and how to determine it, let’s review what factors are and how to determine the greatest common factor of two numbers.
What Is a Common Factor?
In mathematics, a factor is a number that divides into another number, evenly or with no remainder. In other words, all the numbers that can divide into a given number without leaving a remainder are known as the factors of that number. For instance, the factors of 18 are 1, 2, 3, 6, 9 and 18. Therefore, 1, 2, 3, 6, 9 and 18 can all divide into 18 equal divisions with no remainder.
Common factors are factors that two or more numbers have in common. For example, the common factors of 12 and 18 are 1, 2, 3, and 6. Common factors are important in mathematics because they can be used to simplify fractions and solve equations.
How to Find the Greatest Common Factor of 18 and 24
There are several methods for finding the greatest common factor of two numbers. However, the prime factorization method is typically the most efficient approach for finding the GCF for two numbers.
To use the prime factorization method, start by writing out the prime factorization of each number. For 18, the prime factorization is 2 x 3 x 3. For 24, the prime factorization is 2 x 2 x 2 x 3. The greatest common factor is the product of the common prime factors, which in this case is 2 x 3, or 6.
Factors of 18
To illustrate how the prime factorization method works, let’s look at the factors of 18. First, you will need to express 18 as the product of its prime factors. The prime numbers that when multiplied together equal 18 are 2, 3 and 3.
The prime factorization of 18 is 2 x 3 x 3. This means that the factors of 18 are 1, 2, 3, 6, 9, and 18. To find the factors of 18, you can simply multiply each of the prime numbers together. For example, 2 x 3 = 6, 3 x 3 = 9, and 2 x 3 x 3 = 18.
Factors of 24
Next, let’s look at the factors of 24. Again, you will need to express 24 as a product of its prime numbers. The prime numbers that when multiplied together equal 24 are 2, 2, 2 and 3.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. These numbers can be used to divide 24 into equal parts. For example, 24 divided by 4 is 6, and 24 divided by 6 is 4. Knowing the factors of 24 can be useful in many mathematical problems.
Using the Prime Factorization Method to Determine the Greatest Common Factor
Now that you have both sets of prime factors for 18 and 24 written down, it’s time to start looking for their greatest common factor. The common factors between 18 and 24 are 2 and 3. Since 3 is the largest common number between 18 and 24, 3 is therefore the greatest common factor. To summarize, when 18 and 24 are expressed as prime factors, their greatest common factor is 3.
Understanding the Greatest Common Factor
The greatest common factor of two numbers gives you an insight as to how the two numbers are related. In general, if two numbers share a common factor then they are related in some way. For instance, the common factor of 18 and 24 is 3. This means that they have some kind of relationship with each other since 3 is a factor of both numbers.
Examples of Calculating the Greatest Common Factor
Let’s look at some additional examples of calculating the greatest common factor. If you want to find the greatest common factor of 28 and 36 then you can use the prime factorization method we reviewed above. When 28 and 36 are expressed as prime factors, the greatest common factor is 4. This means that the largest number that can divide evenly into both 28 and 36 is 4.
Graphing the Factors of 18 and 24
To gain an even better understanding of how 18 and 24 are related, you can graph their factors on a simple grid. On this graph you’ll see how each of their factors overlap with one another. From this graph you will be able to identify which factors are shared between both numbers and which factors are exclusive to each one.
Benefits of Knowing the Greatest Common Factor
By understanding the greatest common factor between two or more numbers you can better understand how they’re related and learn to solve a variety of mathematical problems more quickly and easily. Knowing the greatest common factor is also incredibly useful when it comes to problem solving in other areas such as engineering and finance.
