# Greatest Common Factor

The greatest common factor (GCF) of two or more non-zero number is the largest positive integer that divides the numbers without a remainder. The greatest common factor is also called the greatest common divisor (GCD) or the Highest Common Factor (HCF).

In these lessons, we will learn how to find the GCF of two or more numbers

• by listing out the factors
• by using the factor tree
• by repetitive division (a faster method)
Related Topics:
More Arithmetic Lessons
Free Math Worksheets

### Listing out the Factors

In this method, we list out the factors of each number and then find the largest among the common factors.

Example :

Find the GCF of 48 and 60

Solution:

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Common factors of 48 and 60 are 1,2,3,4,6,12.
The greatest factor is 12. So the GCF of 48 and 60 is 12.

How to find the GCF by listing out the factors?
Example:
Find the GCF of 12 and 8, 25 and 20, 5 and 12, 6 and 12. How to find the greatest common factor of 16 and 20 by listing out the factors?

### Factor Trees

In this method, we use the factor tree to find the prime factors of each number. We then find the common prime factors and multiply them to get the greatest common factor.

How to find the Greatest Common Factor between two numbers by using factor trees?
Example:
Find the GCF of 30 and 42. Find the greatest common factor by using prime factorization (factor tree)
Example:
Find the GCF of 18 and 24, 72 and 90.

Greatest Common Factor of 3 Numbers using a Factor Tree
Here we find the Greatest Common Factor ( GCF ) of three numbers using a factor tree.
Example:
Find the GCF of 24, 32 and 72.

### Repetitive Division

When the numbers are large, using the lists to find the GCF can be slow and tedious. A faster method would be to use repetitive division to find the highest common factors.

Example :

Find the GCF of 48 and 60

The GCF of 48 and 60 is obtained by multiplying the numbers in the left column:
4 × 3 = 12

How to find the GCF of 24 and 36 using repetitive division?
Find the greatest common factor (GCF) for a set of numbers using the upside down birthday cake method (repetitive division)
Example:
Find the GCF of 12 and 42, 32 and 96.

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