How do you find the GCF of a monomial?

Answer 1

Let's try one.

30x2y3z4 + 42x4y5z2

Do the numbers first.

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6

For the variables, select the lowest exponent.

The GCF of the above expression is 6x2y3z2

Answer 2

Let's try one.

30x2y3z4 + 42x4y5z2

Do the numbers first.

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6

For the variables, select the lowest exponent.

The GCF of the above expression is 6x2y3z2

Answer 3

Example: 30x2y + 42xy2

Factor the whole numbers.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6

Look at the variables. You have x, x, y on one side and x, y, y on the other. Each side has at least an x and a y.

The GCF of this given expression is 6xy.

Answer 4

To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together. Bam! The GCF!

Answer 5

If, in an expression p + q, GCF(p, q) = f then p = f*x and q = f*y for some integers x and y.Then p + q = f*(x + y).