15b3 , 7b4

Since 15b3,7b4 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 15b3,7b4:

1. Find the GCF for the numerical part 15,7

2. Find the GCF for the variable part b3,b4

3. Multiply the values together

Find the common factors for the numerical part:

15,7

The factors for 15 are all numbers between 1 and 15, which divide 15 evenly.

Check numbers between 1 and 15

Find the factor pairs of 15 where x⋅y=15.

xy11535

List the factors for 15.

1,3,5,15

1,3,5,15

The factors for 7 are all numbers between 1 and 7, which divide 7 evenly.

Check numbers between 1 and 7

Find the factor pairs of 7 where x⋅y=7.

xy17

List the factors for 7.

1,7

1,7

List all the factors for 15,7 to find the common factors.

15: 1,3,5,15

7: 1,7

The common factors for 15,7 are 1.

1

The GCF for the numerical part is 1.

GCFNumerical=1

Next, find the common factors for the variable part:

b3,b4

The factors for b3 are b⋅b⋅b.

b⋅b⋅b

The factors for b4 are b⋅b⋅b⋅b.

b⋅b⋅b⋅b

List all the factors for b3,b4 to find the common factors.

b3=b⋅b⋅b

b4=b⋅b⋅b⋅b

The common factors for the variables b3,b4 are b⋅b⋅b.

b⋅b⋅b

The GCF for the variable part is b3.

GCFVariable=b3

Multiply the GCF of the numerical part 1 and the GCF of the variable part b3.

b3

Find the GCF 15b^3 , 7b^4