# Find the GCF 18x , 21 , 9x^2 18x , 21 , 9×2
Since 18x,21,9×2 contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.
Steps to find the GCF for 18x,21,9×2:
1. Find the GCF for the numerical part 18,21,9
2. Find the GCF for the variable part x1,x2
3. Multiply the values together
Find the common factors for the numerical part:
18,21,9
The factors for 18 are 1,2,3,6,9,18.
The factors for 18 are all numbers between 1 and 18, which divide 18 evenly.
Check numbers between 1 and 18
Find the factor pairs of 18 where x⋅y=18.
xy1182936
List the factors for 18.
1,2,3,6,9,18
1,2,3,6,9,18
The factors for 21 are 1,3,7,21.
The factors for 21 are all numbers between 1 and 21, which divide 21 evenly.
Check numbers between 1 and 21
Find the factor pairs of 21 where x⋅y=21.
xy12137
List the factors for 21.
1,3,7,21
1,3,7,21
The factors for 9 are 1,3,9.
The factors for 9 are all numbers between 1 and 9, which divide 9 evenly.
Check numbers between 1 and 9
Find the factor pairs of 9 where x⋅y=9.
xy1933
List the factors for 9.
1,3,9
1,3,9
List all the factors for 18,21,9 to find the common factors.
18: 1,2,3,6,9,18
21: 1,3,7,21
9: 1,3,9
The common factors for 18,21,9 are 1,3.
1,3
The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors 1,3 is 3.
3
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