a4b10c3 , a12c4d2

Since a4b10c3,a12c4d2 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 a4b10c3,a12c4d2:

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

2. Find the GCF for the variable part a4,b10,c3,a12,c4,d2

3. Multiply the values together

Find the common factors for the numerical part:

1,1

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

Check numbers between 1 and 1

Find the factor pairs of 1 where x⋅y=1.

xy11

List the factors for 1.

1

1

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

Check numbers between 1 and 1

Find the factor pairs of 1 where x⋅y=1.

xy11

List the factors for 1.

1

1

List all the factors for 1,1 to find the common factors.

1: 1

1: 1

The common factors for 1,1 are 1.

1

The GCF for the numerical part is 1.

GCFNumerical=1

Next, find the common factors for the variable part:

a4,b10,c3,a12,c4,d2

The factors for a4 are a⋅a⋅a⋅a.

a⋅a⋅a⋅a

The factors for b10 are b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b.

b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b

The factors for c3 are c⋅c⋅c.

c⋅c⋅c

The factors for a12 are a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a.

a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a

The factors for c4 are c⋅c⋅c⋅c.

c⋅c⋅c⋅c

The factors for d2 are d⋅d.

d⋅d

List all the factors for a4,b10,c3,a12,c4,d2 to find the common factors.

a4=a⋅a⋅a⋅a

b10=b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b

c3=c⋅c⋅c

a12=a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a⋅a

c4=c⋅c⋅c⋅c

d2=d⋅d

The common factors for the variables a4,b10,c3,a12,c4,d2 are a⋅a⋅a⋅a⋅c⋅c⋅c.

a⋅a⋅a⋅a⋅c⋅c⋅c

The GCF for the variable part is a4c3.

GCFVariable=a4c3

Multiply the GCF of the numerical part 1 and the GCF of the variable part a4c3.

a4c3

Find the GCF a^4b^10c^3 , a^12c^4d^2