-30xy2 , 15x3y3⋅(60x2y3)

Multiply x3 by x2 by adding the exponents.

Move x2.

-30xy2,15(x2x3)y3⋅(60y3)

Use the power rule aman=am+n to combine exponents.

-30xy2,15×2+3y3⋅(60y3)

Add 2 and 3.

-30xy2,15x5y3⋅(60y3)

-30xy2,15x5y3⋅(60y3)

Multiply y3 by y3 by adding the exponents.

Move y3.

-30xy2,15×5(y3y3)⋅60

Use the power rule aman=am+n to combine exponents.

-30xy2,15x5y3+3⋅60

Add 3 and 3.

-30xy2,15x5y6⋅60

-30xy2,15x5y6⋅60

Multiply 60 by 15.

-30xy2,900x5y6

-30xy2,900x5y6

Since -30xy2,900x5y6 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 -30xy2,900x5y6:

1. Find the GCF for the numerical part -30,900

2. Find the GCF for the variable part x1,y2,x5,y6

3. Multiply the values together

Find the common factors for the numerical part:

-30,900

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.

List the factors for -30.

-30,-15,-10,-6,-5,-3,-2,-1,1,2,3,5,6,10,15,30

-30,-15,-10,-6,-5,-3,-2,-1,1,2,3,5,6,10,15,30

The factors for 900 are all numbers between 1 and 900, which divide 900 evenly.

Check numbers between 1 and 900

Find the factor pairs of 900 where x⋅y=900.

xy19002450330042255180615091001090127515601850204525363030

List the factors for 900.

1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

List all the factors for -30,900 to find the common factors.

-30: -30,-15,-10,-6,-5,-3,-2,-1,1,2,3,5,6,10,15,30

900: 1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

The common factors for -30,900 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:

x,y2,x5,y6

The factor for x1 is x itself.

x

The factors for y2 are y⋅y.

y⋅y

The factors for x5 are x⋅x⋅x⋅x⋅x.

x⋅x⋅x⋅x⋅x

The factors for y6 are y⋅y⋅y⋅y⋅y⋅y.

y⋅y⋅y⋅y⋅y⋅y

List all the factors for x1,y2,x5,y6 to find the common factors.

x1=x

y2=y⋅y

x5=x⋅x⋅x⋅x⋅x

y6=y⋅y⋅y⋅y⋅y⋅y

The common factors for the variables x1,y2,x5,y6 are x⋅y⋅y.

x⋅y⋅y

The GCF for the variable part is xy2.

GCFVariable=xy2

Multiply the GCF of the numerical part 30 and the GCF of the variable part xy2.

30xy2

Find the GCF -30xy^2 , 15x^3y^3*(60x^2y^3)