# Find the GCF 64a^8b^4c^7 , 56a^5b^8

64a8b4c7 , 56a5b8
Since 64a8b4c7,56a5b8 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 64a8b4c7,56a5b8:
1. Find the GCF for the numerical part 64,56
2. Find the GCF for the variable part a8,b4,c7,a5,b8
3. Multiply the values together
Find the common factors for the numerical part:
64,56
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 56 are 1,2,4,7,8,14,28,56.
The factors for 56 are all numbers between 1 and 56, which divide 56 evenly.
Check numbers between 1 and 56
Find the factor pairs of 56 where x⋅y=56.
xy15622841478
List the factors for 56.
1,2,4,7,8,14,28,56
1,2,4,7,8,14,28,56
List all the factors for 64,56 to find the common factors.
64: 1,2,4,8,16,32,64
56: 1,2,4,7,8,14,28,56
The common factors for 64,56 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:
a8,b4,c7,a5,b8
The factors for a8 are 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 c7 are c⋅c⋅c⋅c⋅c⋅c⋅c.
c⋅c⋅c⋅c⋅c⋅c⋅c
The factors for a5 are a⋅a⋅a⋅a⋅a.
a⋅a⋅a⋅a⋅a
The factors for b8 are b⋅b⋅b⋅b⋅b⋅b⋅b⋅b.
b⋅b⋅b⋅b⋅b⋅b⋅b⋅b
List all the factors for a8,b4,c7,a5,b8 to find the common factors.
a8=a⋅a⋅a⋅a⋅a⋅a⋅a⋅a
b4=b⋅b⋅b⋅b
c7=c⋅c⋅c⋅c⋅c⋅c⋅c
a5=a⋅a⋅a⋅a⋅a
b8=b⋅b⋅b⋅b⋅b⋅b⋅b⋅b
The common factors for the variables a8,b4,c7,a5,b8 are a⋅a⋅a⋅a⋅a⋅b⋅b⋅b⋅b.
a⋅a⋅a⋅a⋅a⋅b⋅b⋅b⋅b
The GCF for the variable part is a5b4.
GCFVariable=a5b4
Multiply the GCF of the numerical part 8 and the GCF of the variable part a5b4.
8a5b4
Find the GCF 64a^8b^4c^7 , 56a^5b^8