The factors of 8 are: 1, 2, 4, 8
The factors of 9 are: 1, 3, 9
Then the greatest common factor is 1.
Step-by-step explanation:How to Find the Greatest Common Factor (GCF)
There are several ways to find the greatest common factor of numbers. The most efficient method you use depends on how many numbers you have, how large they are and what you will do with the result.
Factoring
To find the GCF by factoring, list out all of the factors of each number or find them with a Factors Calculator. The whole number factors are numbers that divide evenly into the number with zero remainder. Given the list of common factors for each number, the GCF is the largest number common to each list.
Example: Find the GCF of 18 and 27The factors of 18 are 1, 2, 3, 6, 9, 18.
The factors of 27 are 1, 3, 9, 27.
The common factors of 18 and 27 are 1, 3 and 9.
The greatest common factor of 18 and 27 is 9.
Example: Find the GCF of 20, 50 and 120
The factors of 20 are 1, 2, 4, 5, 10, 20.
The factors of 50 are 1, 2, 5, 10, 25, 50.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
The common factors of 20, 50 and 120 are 1, 2, 5 and 10. (Include only the factors common to all three numbers.)
The greatest common factor of 20, 50 and 120 is 10.Prime Factorization
To find the GCF by prime factorization, list out all of the prime factors of each number or find them with a Prime Factors Calculator. List the prime factors that are common to each of the original numbers. Include the highest number of occurrences of each prime factor that is common to each original number. Multiply these together to get the GCF.
You will see that as numbers get larger the prime factorization method may be easier than straight factoring.
Example: Find the GCF (18, 27)
The prime factorization of 18 is 2 x 3 x 3 = 18.
The prime factorization of 27 is 3 x 3 x 3 = 27.
The occurrences of common prime factors of 18 and 27 are 3 and 3.
So the greatest common factor of 18 and 27 is 3 x 3 = 9.
Example: Find the GCF (20, 50, 120)
The prime factorization of 20 is 2 x 2 x 5 = 20.
The prime factorization of 50 is 2 x 5 x 5 = 50.
The prime factorization of 120 is 2 x 2 x 2 x 3 x 5 = 120.The occurrences of common prime factors of 20, 50 and 120 are 2 and 5.
So the greatest common factor of 20, 50 and 120 is 2 x 5 = 10.
