Greatest Common Factor
2026-02-28 08:33 Diff
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In this section, let’s see how to find the GCF of any two or more numbers. The common methods used to find the GCF are:
 

  • Listing Out Common Factors
     
  • Prime Factorization
     
  • Division Method
     

Listing Out Common Factors

In this method, we write down the factors of the given number and identify the common factors to find the GCF. Follow these steps to find the GCF of any two or more numbers using listing out common factors:

Step 1: Write down all the factors of the given number.


Step 2: Identifying the common factors from the list. 


Step 3: The largest number from the common factors is the GCF.  

Now, let’s find the GCF of 81 and 72.


Step 1: List the factors of 81 and 72.
 

The factors of 81 are 1, 3, 9, 27, 81.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Step 2: Identify the common factors from the list. 


The common factors of 81 and 72 are 1, 3, 9.

Step 3: Find the largest number among the common factors


Here, the largest common factor is 9.


So, the GCF of 81 and 72 is 9.

Prime Factorization

In this method, the given number is broken down into its prime factors. Then the common prime factors are identified and multiplied to determine the GCF. Follow the steps mentioned below to find the GCF: 


Step 1: Breaking the given number into its prime factors.


Step 2: Identify the common prime.


Step 3: Multiplying the common prime factors. 


Now, let’s find the GCF of 28 and 24.


Step 1: Breaking the given number into its prime factors


The prime factorization of 28 is \(2 × 2 × 7 = 2² × 7\).


The prime factorization of 24 is \(2 × 2 × 2 × 3 = 2³ × 3\).


Step 2: Identifying the common prime.


The common prime factor is 2.

Step 3: Take the smallest power of the common factor.

Smallest power of \(2 = 2² = 4\).

GCF of 28 and 24 is 4. 

Division Method


In this method, we divide the larger number by its smaller counterpart. Then the remainder is divided by the previous divisor. The process is repeated until the remainder is zero. Follow the steps given below to find the GCF using the division method:


Step 1: Dividing the largest number by the smallest number.


Step 2: If the remainder is 0 in the first step, then the divisor in step 1 will be the dividend in step 2. Now, the remainder will be the new divisor.

 
Step 3: When the remainder becomes 0, the divisor will be the GCF. If not, the process will be repeated.


Now, let’s find the GCF of 54 and 42.


Step 1: Dividing the largest number by the smallest number. So dividing 54 by 42, then the remainder is 12. 


Step 2: Now divide the previous divisor 42 by the remainder 12.
\(42 ÷ 12 = 3\) remainder 6. 

Step 3: Divide the previous divisor 12 by the new remainder 6.
\(12 ÷ 6 = 2\) remainder 0.

Step 4: When the remainder becomes 0, the divisor is the GCF. Therefor, the GCF of 54 and 42 is 6.