7xy2⋅(49×2) , 35xy2

Multiply x by x2 by adding the exponents.

Move x2.

7(x2x)y2⋅49,35xy2

Multiply x2 by x.

Raise x to the power of 1.

7(x2x)y2⋅49,35xy2

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

7×2+1y2⋅49,35xy2

7×2+1y2⋅49,35xy2

Add 2 and 1.

7x3y2⋅49,35xy2

7x3y2⋅49,35xy2

Multiply 49 by 7.

343x3y2,35xy2

343x3y2,35xy2

Since 343x3y2,35xy2 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 343x3y2,35xy2:

1. Find the GCF for the numerical part 343,35

2. Find the GCF for the variable part x3,y2,x1,y2

3. Multiply the values together

Find the common factors for the numerical part:

343,35

The factors for 343 are all numbers between 1 and 343, which divide 343 evenly.

Check numbers between 1 and 343

Find the factor pairs of 343 where x⋅y=343.

xy1343749

List the factors for 343.

1,7,49,343

1,7,49,343

The factors for 35 are all numbers between 1 and 35, which divide 35 evenly.

Check numbers between 1 and 35

Find the factor pairs of 35 where x⋅y=35.

xy13557

List the factors for 35.

1,5,7,35

1,5,7,35

List all the factors for 343,35 to find the common factors.

343: 1,7,49,343

35: 1,5,7,35

The common factors for 343,35 are 1,7.

1,7

The GCF for the numerical part is 7.

GCFNumerical=7

Next, find the common factors for the variable part:

x3,y2,x,y2

The factors for x3 are x⋅x⋅x.

x⋅x⋅x

The factors for y2 are y⋅y.

y⋅y

The factor for x1 is x itself.

x

The factors for y2 are y⋅y.

y⋅y

List all the factors for x3,y2,x1,y2 to find the common factors.

x3=x⋅x⋅x

y2=y⋅y

x1=x

y2=y⋅y

The common factors for the variables x3,y2,x1,y2 are x⋅y⋅y.

x⋅y⋅y

The GCF for the variable part is xy2.

GCFVariable=xy2

Multiply the GCF of the numerical part 7 and the GCF of the variable part xy2.

7xy2

Find the GCF 7xy^2*(49x^2) , 35xy^2