Greatest Common Factor of 18 and 27
Factors of 18-1, 2, 3, 6, 9, 18 {Six}
Factors of 27-1, 3, 9, 27 {Four}
The common factors of 18 and 27 are 1, 3, and 9 {crop up in both numbers 18 and 27}
Among these numbers, 9 is the greatest (largest) number or Greatest Common Factor {GCF}
Following are the three methods for finding the greatest common factor of two numbers:
Listing out common factors
Prime factorization and finally
Division method
Example: What is the GCF of 30 and 42
Step 1 - List out the factors of each number
Factors of 30-1 2 3 5 6 10 15 and 30 {Eight}
Factors of 42-1 2 3 6 7 14 21 and 42 {Eight}
Step 2 - Mark all the common factors {numbers that crop up into 2 or more numbers}
Common Factors-1 2 3 and 6 {crop up}
Greatest Common Factor {GCF} of 30 and 42 is 6
Find the GCF of 6, 12, and 36 by using the listing factors method
Factors of 6-1 2 3 and 6 {Four}
Factors of 12-1 2 3 4 6 and 12 {Six}
Factors of 36-1 2 3 4 6 9 12 18 and 36 {Nine}
Common Factors of 6, 12, and 36 are 1 2 3 and 6
GCF of 6 12 and 36 is 6
