Find the GCF 60y^8 , 40y^4 , 20y^5 , 80y^5

Math
60y8 , 40y4 , 20y5 , 80y5
Since 60y8,40y4,20y5,80y5 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 60y8,40y4,20y5,80y5:
1. Find the GCF for the numerical part 60,40,20,80
2. Find the GCF for the variable part y8,y4,y5,y5
3. Multiply the values together
Find the common factors for the numerical part:
60,40,20,80
The factors for 60 are 1,2,3,4,5,6,10,12,15,20,30,60.
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The factors for 60 are all numbers between 1 and 60, which divide 60 evenly.
Check numbers between 1 and 60
Find the factor pairs of 60 where x⋅y=60.
xy160230320415512610
List the factors for 60.
1,2,3,4,5,6,10,12,15,20,30,60
1,2,3,4,5,6,10,12,15,20,30,60
The factors for 40 are 1,2,4,5,8,10,20,40.
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The factors for 40 are all numbers between 1 and 40, which divide 40 evenly.
Check numbers between 1 and 40
Find the factor pairs of 40 where x⋅y=40.
xy14022041058
List the factors for 40.
1,2,4,5,8,10,20,40
1,2,4,5,8,10,20,40
The factors for 20 are 1,2,4,5,10,20.
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The factors for 20 are all numbers between 1 and 20, which divide 20 evenly.
Check numbers between 1 and 20
Find the factor pairs of 20 where x⋅y=20.
xy12021045
List the factors for 20.
1,2,4,5,10,20
1,2,4,5,10,20
The factors for 80 are 1,2,4,5,8,10,16,20,40,80.
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The factors for 80 are all numbers between 1 and 80, which divide 80 evenly.
Check numbers between 1 and 80
Find the factor pairs of 80 where x⋅y=80.
xy180240420516810
List the factors for 80.
1,2,4,5,8,10,16,20,40,80
1,2,4,5,8,10,16,20,40,80
List all the factors for 60,40,20,80 to find the common factors.
60: 1,2,3,4,5,6,10,12,15,20,30,60
40: 1,2,4,5,8,10,20,40
20: 1,2,4,5,10,20
80: 1,2,4,5,8,10,16,20,40,80
The common factors for 60,40,20,80 are 1,2,4,5,10,20.
1,2,4,5,10,20
The GCF for the numerical part is 20.
GCFNumerical=20
Next, find the common factors for the variable part:
y8,y4,y5,y5
The factors for y8 are y⋅y⋅y⋅y⋅y⋅y⋅y⋅y.
y⋅y⋅y⋅y⋅y⋅y⋅y⋅y
The factors for y4 are y⋅y⋅y⋅y.
y⋅y⋅y⋅y
The factors for y5 are y⋅y⋅y⋅y⋅y.
y⋅y⋅y⋅y⋅y
List all the factors for y8,y4,y5,y5 to find the common factors.
y8=y⋅y⋅y⋅y⋅y⋅y⋅y⋅y
y4=y⋅y⋅y⋅y
y5=y⋅y⋅y⋅y⋅y
y5=y⋅y⋅y⋅y⋅y
The common factors for the variables y8,y4,y5,y5 are y⋅y⋅y⋅y.
y⋅y⋅y⋅y
The GCF for the variable part is y4.
GCFVariable=y4
Multiply the GCF of the numerical part 20 and the GCF of the variable part y4.
20y4
Find the GCF 60y^8 , 40y^4 , 20y^5 , 80y^5

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