Examples of Greatest Common Factor

There are various examples we can consider for calculation of Greatest Common Factor. Let’s consider the following examples.

Greatest Common Factor of 12 and 18

Let’s find the GCF of 12 and 18.

• Factors of 12 = 1, 2, 3, 4, 6, 12
• Factors of 18 = 1, 2, 3, 6, 9, 18

Between 12 and 18, 6 is the greatest common number. Considering that all number factors may be found between 1 and 6. The number 6 is by far the larger of these two numbers. Thus, these integers have a GCF of 6.

Greatest Common Factor of 24 and 40

The numbers 24 and 40 are provided. We’ll determine each of these numbers’ components.

• Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40

In this case, the common factors for the numbers 24 and 40 are 1, 2, 4, and 8. The greatest common factor among all of these is 8, hence GCF(24 and 40) = 8.

Greatest Common Factor of 15 and 20

• Prime factors of 15: 1, 3, 5, 15
• Prime factors of 20: 1, 2, 4, 5, 10, 20

In this case, the common factors for the numbers 15 and 20 are 1 and 5. The greatest common factor among all of these is 5, hence GCF(15 and 20) = 5.

Greatest Common Factor of Monomial

The highest word that divides two or more monomials without remainder is the greatest common factor (GCF). Finding the biggest word that splits equally into two or more monomials is the Greatest Common Factor (GCF) of monomials.

For example, take the monomials 6x²y and 8xy³:

Step 1: Determine the prime factors of each coefficient and variable term .

• The prime factors for 6x²y are 2, 3, x², and y.
• The prime factors for 8xy³ are 2, 2, 2, x, y³.

Step 2: Find the common factors. The common factors in this situation are 2, x, and y.

Step 3: Find the exponent with the lowest exponent for each common factor. It’s x¹ and y¹ in this case.

Step 4: Divide the common components by the lowest exponent: 2xy.

As a result, the GCF of  6x²y and 8xy³ is 2xy. This GCF is essential for simplifying monomial expressions and factoring polynomial expressions.

Greatest Common Factor or GCF is the largest positive integer that evenly divides two or more integers without leaving a residual. In simple words, the Greatest Common Factor is the largest value that can be used to divide these numbers and get whole numbers. 

Greatest Common Factor is a fundamental idea in mathematics and is essential for equation solving, simplifying fractions, and finding common components in a variety of mathematical settings.

In this article, we will discuss the concept of the Greatest Common Factor in detail including definition, methods to find the Greatest Common Factor, and various solved examples for calculating the Greatest Common Factor.