What is the greatest common factor of the following monomials?
20xyz, 30x^2z, 40xyz^2
a) 5y^2
b) 10x^2
c) 5xyz
d)10xz
b
Nope, there is no x^2 term in 20xyz
To find the greatest common factor (GCF) of the given monomials, we need to identify the highest power of each variable that appears in all the monomials.
First, let's break down the given monomials into their prime factors:
20xyz = (2 * 2 * 5 * x * y * z)
30x^2z = (2 * 3 * 5 * x * x * z)
40xyz^2 = (2 * 2 * 2 * 5 * x * y * z * z)
Next, compare the factors of each variable:
For the variable 'x', we have:
- In 20xyz: x
- In 30x^2z: x * x
- In 40xyz^2: x
The highest power of 'x' that appears in all the monomials is x * x, which is x^2.
For the variable 'y', we have:
- In 20xyz: y
- In 30x^2z: Doesn't have 'y'
- In 40xyz^2: y
Therefore, the highest power of 'y' that appears in all the monomials is y.
For the variable 'z', we have:
- In 20xyz: z
- In 30x^2z: z
- In 40xyz^2: z * z
The highest power of 'z' that appears in all the monomials is z * z, which is z^2.
Finally, let's examine the numerical coefficients (20, 30, 40). The GCF of the coefficients is 10, which is a common factor of all the coefficients.
In summary, the GCF of the given monomials is:
GCF of the numerical coefficients * GCF of the variables = 10 * x^2 * y * z^2
Comparing the GCF with the given options, we find that the correct answer is b) 10x^2.