GCF of Two Numbers

What Are The Factors?

In Mathematics, factors are those numbers which on multiplication gives us the original number. Factors are always whole numbers.  Only the decimal numbers and fractions are not considered as factors.  To find factors, you must be familiar with the multiplication table so it will be easy to find them. The numbers can be factorized into different combinations. There are various methods to find the factors of the number. They are the factorization method, the prime factorization method, division method, and the divisibility method. Here, we are going to discuss what is the greatest common factor and how to find it.

Greatest Common Factor

The factor which is common and largest between the two numbers is called the greatest common factor. It is the largest number which divides them giving the answer as the whole number. 

The greatest common factor (GCF) is also known as the highest common factor (HCF).

For example, find the greatest common factor (GCF) of 12 and 20.

The Factors of 12 are 2 × 2 × 3

The Factors of 20 are 2 × 2 × 5

Then common factors are 2 so that the greatest common factor (GCF) of 12 and 20 is 2.

Example - Find the greatest common factor (GCF) of 20 and 30.

The Factors of 20 = 2 × 2 × 5

The Factors of 30 = 2 × 3 × 5 

Here the common factors are 2 and 5 so the greatest common factor (GCF) of 20 and 30 is 2 × 5= 10.


Factoring Greatest Common Factor

In this, we will use the factorization method to list out all the factors of the given numbers. In the factorization method, the factors are found by considering two numbers which on multiplication gives us the original number.

By calculating factors, it will be easy to find the greatest common factor (GCF) and the least common multiple (LCM).

Example 1- Find the greatest common factor (GCF)of 12 and 18 using the factoring method.

Then Factors of 12 are 1, 2, 3, 4, 6, 12.

Because 1 × 12 = 12, 2 × 6 = 12, and 3 × 4 = 12

Then Factors of 18 are 1, 2, 3, 6, 9, 18.

Because 1 × 18 = 18, 2 × 9 = 18, and 3 × 6 = 19.

Thus, the common factors between 12 and 18 are 1, 2, 3, 6.

The largest common factor is 6.

Therefore, the greatest common factor (GCF) of 12 and 18 is 6.

Example-2

Find out the least common multiple (LCM) of 24 and 36.

Then Factors of 24 are 2 × 2 × 2 × 3.

Then Factors of 36 are 2 × 2 × 3 × 3.

A least common multiple (LCM) of 24 and 36 is 2 × 2 × 2 × 2 × 3 = 72.

Find the greatest common factor (GCF) of 8, 18,28, and 48.

Solution:

First, we will find factors of all the numbers,

Then Factors of 8 = 1, 2, 4, 8.

Then Factors of 18 = 1, 2, 3, 6, 9, 18.

Then Factors of 28 = 1, 2, 4, 7, 14, 28.

Then Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Now we will find the common factors between these numbers.

The largest common factor of 8, 18, 28, 48 is 2. Because factors 1 and 2 are found to be the common factors of these numbers. Between 1 and 2 factors 2 is the largest common factor, therefore, the greatest common factor (GCF) is 2.

FAQ (Frequently Asked Questions)

1. How to find the greatest common factor?

The steps to find the greatest common factors are:

  1. First, we need to list down two numbers for which we need to find the greatest common factor.

  2. We will find the prime factors of both the numbers.

  3. Then we will list down the common factors between these two numbers.

  4. After listing down the common factors, we will multiply the common factors.

  5. The result obtained from this will be the greatest common factor of the two numbers which we have considered.

  6. If there are no common factors between the two numbers, then 1 is considered as the greatest common factor.

2. What is the difference between the greatest common factor and the least common multiple?

The greatest common factor (GCF) is defined as the largest factor which is common between two numbers. The greatest common factor (GCF) is also known as the highest common factor (HCF). Least common multiple (LCM) is defined as the smallest number which is the multiple of all the numbers. The least common multiple values should be non zero. These are the factorization method to list out all the factors of the given numbers.