# Find the GCF 30x^5 , 110x^7*(60x^8)

30×5 , 110×7⋅(60×8)
Simplify each term.
Rewrite using the commutative property of multiplication.
30×5,110⋅(60(x7x8))
Multiply x7 by x8 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
30×5,110⋅(60×7+8)
30×5,110⋅(60×15)
30×5,110⋅(60×15)
Multiply 110 by 60.
30×5,6600×15
30×5,6600×15
Since 30×5,6600×15 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 30×5,6600×15:
1. Find the GCF for the numerical part 30,6600
2. Find the GCF for the variable part x5,x15
3. Multiply the values together
Find the common factors for the numerical part:
30,6600
The factors for 30 are 1,2,3,5,6,10,15,30.
The factors for 30 are all numbers between 1 and 30, which divide 30 evenly.
Check numbers between 1 and 30
Find the factor pairs of 30 where x⋅y=30.
xy13021531056
List the factors for 30.
1,2,3,5,6,10,15,30
1,2,3,5,6,10,15,30
The factors for 6600 are 1,2,3,4,5,6,8,10,11,12,15,20,22,24,25,30,33,40,44,50,55,60,66,75,88,100,110,120,132,150,165,200,220,264,275,300,330,440,550,600,660,825,1100,1320,1650,2200,3300,6600.
The factors for 6600 are all numbers between 1 and 6600, which divide 6600 evenly.
Check numbers between 1 and 6600
Find the factor pairs of 6600 where x⋅y=6600.
xy1660023300322004165051320611008825106601160012550154402033022300242752526430220332004016544150501325512060110661007588
List the factors for 6600.
1,2,3,4,5,6,8,10,11,12,15,20,22,24,25,30,33,40,44,50,55,60,66,75,88,100,110,120,132,150,165,200,220,264,275,300,330,440,550,600,660,825,1100,1320,1650,2200,3300,6600
1,2,3,4,5,6,8,10,11,12,15,20,22,24,25,30,33,40,44,50,55,60,66,75,88,100,110,120,132,150,165,200,220,264,275,300,330,440,550,600,660,825,1100,1320,1650,2200,3300,6600
List all the factors for 30,6600 to find the common factors.
30: 1,2,3,5,6,10,15,30
6600: 1,2,3,4,5,6,8,10,11,12,15,20,22,24,25,30,33,40,44,50,55,60,66,75,88,100,110,120,132,150,165,200,220,264,275,300,330,440,550,600,660,825,1100,1320,1650,2200,3300,6600
The common factors for 30,6600 are 1,2,3,5,6,10,15,30.
1,2,3,5,6,10,15,30
The GCF for the numerical part is 30.
GCFNumerical=30
Next, find the common factors for the variable part:
x5,x15
The factors for x5 are x⋅x⋅x⋅x⋅x.
x⋅x⋅x⋅x⋅x
The factors for x15 are x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x.
x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
List all the factors for x5,x15 to find the common factors.
x5=x⋅x⋅x⋅x⋅x
x15=x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x⋅x
The common factors for the variables x5,x15 are x⋅x⋅x⋅x⋅x.
x⋅x⋅x⋅x⋅x
The GCF for the variable part is x5.
GCFVariable=x5
Multiply the GCF of the numerical part 30 and the GCF of the variable part x5.
30×5
Find the GCF 30x^5 , 110x^7*(60x^8)