Question

Find the greatest common factor for the list of monomials. 20x4y2z, 4x4y, 60x3y3 The greatest common factor is

Answer 1

The greatest common factor for the monomials 20x^4y^2z, 4x^4y, and 60x^3y^3 is 4x^3y, obtained by finding the lowest powers of the common factors.

Step-by-step explanation:

The greatest common factor (GCF) of a list of monomials is the highest monomial that divides each monomial in the list without leaving a remainder. To find the GCF of the monomials 20x4y2z, 4x4y, and 60x3y3, we break each monomial into its prime factors and variable components:

1. 20x4y2z = 22 × 5 × x4 × y2 × z
2. 4x4y = 22 × x4 × y
3. 60x3y3 = 22 × 3 × 5 × x3 × y3

Now we identify the lowest powers of the common prime factors and variables:

• The lowest power of 2 is 22.
• The lowest power of x is x3.
• The lowest power of y is y.

Multiplying these together gives us the GCF:

22 × x3 × y = 4x3y

This is the greatest common factor for the given list of monomials.

Answer 2

The monomials given are:

`\begin{gathered} 20x^4y^2z \\ 4x^4y \\ 60x^3y^3 \end{gathered}`

First, we will write each monomial as a product of each individual factors. So,

`\begin{gathered} 20x^4y^2z=2\cdot2\cdot5\cdot x\cdot x\cdot x\cdot x\cdot y\cdot y\cdot z \\ 4x^4y=2\cdot2\cdot x\cdot x\cdot x\cdot x\cdot y \\ 60x^3y^3=2\cdot2\cdot3\cdot5\cdot x\cdot x\cdot x\cdot y\cdot y\cdot y \end{gathered}`

Now, we will circle the factors/numbers that are common to all 3 monomials.

That is,

Thus, we can write the GCF as,

`\begin{gathered} 2\cdot2\cdot x\cdot x\cdot x\cdot y \\ =4x^3y \end{gathered}`