# Find the GCF 64a^10b^4 , 88a^6b^10

64a10b4 , 88a6b10
Since 64a10b4,88a6b10 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 64a10b4,88a6b10:
1. Find the GCF for the numerical part 64,88
2. Find the GCF for the variable part a10,b4,a6,b10
3. Multiply the values together
Find the common factors for the numerical part:
64,88
The factors for 64 are 1,2,4,8,16,32,64.
The factors for 64 are all numbers between 1 and 64, which divide 64 evenly.
Check numbers between 1 and 64
Find the factor pairs of 64 where x⋅y=64.
xy16423241688
List the factors for 64.
1,2,4,8,16,32,64
1,2,4,8,16,32,64
The factors for 88 are 1,2,4,8,11,22,44,88.
The factors for 88 are all numbers between 1 and 88, which divide 88 evenly.
Check numbers between 1 and 88
Find the factor pairs of 88 where x⋅y=88.
xy188244422811
List the factors for 88.
1,2,4,8,11,22,44,88
1,2,4,8,11,22,44,88
List all the factors for 64,88 to find the common factors.
64: 1,2,4,8,16,32,64
88: 1,2,4,8,11,22,44,88
The common factors for 64,88 are 1,2,4,8.
1,2,4,8
The GCF for the numerical part is 8.
GCFNumerical=8
Next, find the common factors for the variable part:
a10,b4,a6,b10
The factors for a10 are a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a.
a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a
The factors for b4 are b⋅b⋅b⋅b.
b⋅b⋅b⋅b
The factors for a6 are a⋅a⋅a⋅a⋅a⋅a.
a⋅a⋅a⋅a⋅a⋅a
The factors for b10 are b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b.
b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b
List all the factors for a10,b4,a6,b10 to find the common factors.
a10=a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a
b4=b⋅b⋅b⋅b
a6=a⋅a⋅a⋅a⋅a⋅a
b10=b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b
The common factors for the variables a10,b4,a6,b10 are a⋅a⋅a⋅a⋅a⋅a⋅b⋅b⋅b⋅b.
a⋅a⋅a⋅a⋅a⋅a⋅b⋅b⋅b⋅b
The GCF for the variable part is a6b4.
GCFVariable=a6b4
Multiply the GCF of the numerical part 8 and the GCF of the variable part a6b4.
8a6b4
Find the GCF 64a^10b^4 , 88a^6b^10