Greatest Common Factor Worksheets

There are six sets of factors & multiples worksheets:

• Factors
  
• Prime Factorization
  
• Greatest Common Factor
  
• Multiples
  
• Least Common Multiple
  
• LCM and GCF
  

Examples, solutions, videos, and worksheets to help Grade 4 students learn how to find the greatest common factor (GCF).

How to find the greatest common factor?

There are two sets of greatest common factor worksheets.

• Greatest Common Factor (Two Numbers).
• Greatest Common Factor (Three Numbers).

Common Factor Method
You can find the greatest common factor (GCF) of two or more numbers by listing out the factors of each number and identifying the common factors. Here’s a step-by-step guide on how to do this:

1. Begin by listing all the factors of each of the numbers for which you want to find the GCF. Factors are the whole numbers that can divide a given number evenly without leaving a remainder. You can start with the number 1 and include the number itself as factors.
2. Compare the lists of factors for each number and identify the factors that are common to all the numbers. These common factors are the ones that appear in the factor lists of all the numbers you are considering.
3. To find the GCF, determine the largest common factor among the numbers. This is the GCF.

Example: Find the GCF of 18 and 24.

1. List the Factors of Each Number
   Factors of 18: 1, 2, 3, 6, 9, 18
   Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
2. Identify the Common Factors
   The common factors of 18 and 24 are 1, 2, 3, and 6.
3. Determine the GCF
   Among the common factors, the largest one is 6. So, the GCF of 18 and 24 is 6.

Prime Factorization Method
Listing out factors is a straightforward method for finding the GCF, especially when dealing with relatively small numbers. However, for larger numbers, the prime factorization method is more efficient. Here’s a step-by-step guide on how to find the GCF of two or more numbers using prime factorization:

1. Express each number as a product of its prime factors. (also called prime factorization)
2. Once you have the prime factorizations, identify the prime factors that are common to all the numbers. These are the prime factors that appear in each number’s factorization.
3. Multiply together all the common prime factors you identified in Step 2. This product is the GCF of the numbers.

Example: Find the GCF of 36 and 48.

1. List the Prime Factors Prime factorization of 36: 2² × 3² Prime factorization of 48: 2⁴ × 3¹
2. Identify Common Prime Factors The common prime factor for 2 is 2² The common prime factor for 3 is 3¹
3. Multiply the Common Prime Factors GCF of 36 and 48 = 2² × 3¹ = 12

This method can be extended to find the GCF of more than two numbers by including the prime factorizations of all the numbers and identifying the common prime factors. The GCF represents the largest number that divides all the given numbers without leaving a remainder.

Have a look at this video if you need to review how to find the Greatest Common Factor.

• How to Find the GCF using Prime Factorization

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Greatest Common Factor Worksheets.

 

More Greatest Common Factor Worksheets

Printable
(Answers on the second page.)
Greatest Common Factor Worksheet #1 (Two Numbers)
Greatest Common Factor Worksheet #2 (Three Numbers)
Greatest Common Factor Worksheet #3 (Larger Numbers)
Greatest Common Factor Worksheet #4 (Larger Numbers)

Online
Prime & Composite Numbers up to 10
Prime & Composite Numbers up to 20

Find Missing Factor
Greatest Common Factor
GCF or HCF

GCF and LCM Word Problems

Related Lessons & Worksheets

Factors & Multiples

More Printable Worksheets

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