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
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
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.
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!
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).
When you simplify each of those expressions you get 120xy, 210xy and 216xy. The GCF of those is 6xy because it divides evenly into all of them.
You need at least two terms to find an LCM.
You need at least two numbers to find a GCF. If that's 16 and 66, the GCF is 2.
You need at least two numbers to find a GCF. If that's 72 and 96, the GCF is 24.
The GCF is 2.
Find the gcf for the coefficients and find the smallest exponential for the variable(s), but the variable must be in all the monomial terms.
4
To find the GCF of each pair of monomials of 10a and lza²b, we can use the following steps: Write the complete factorization of each monomial, including the constants and the variables with their exponents. 10a = 2 ⋅ 5 ⋅ a lza²b = lz ⋅ a ⋅ a ⋅ b Identify the common factors in both monomials. These are the factors that appear in both factorizations with the same or lower exponent. The common factors are : a Multiply the common factors to get the GCF. GCF = a Therefore, the GCF of each pair of monomial of 10a and lza²b = a
To find the GCF of each pair of monomial of -8x³ and 10a²b², we can use the following steps: Write the complete factorization of each monomial, including the constants and the variables with their exponents. -8x³ = -1 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ x ⋅ x ⋅ x 10a²b² = 2 ⋅ 5 ⋅ a ⋅ a ⋅ b ⋅ b Identify the common factors in both monomials. These are the factors that appear in both factorizations with the same or lower exponent. The common factors are: 2 Multiply the common factors to get the GCF. GCF = 2 Therefore, the GCF of each pair of monomial of -8x³ and 10a²b² is 2.
gcf is Greatest Common Factor. It means what is the largest value that can go into what you are factoring.
To find the GCF of each pair of monomial of 8ab³ and 10a²b², we can use the following steps: Write the complete factorization of each monomial, including the constants and the variables with their exponents. 8ab³ = 2 ⋅ 2 ⋅ 2 ⋅ a ⋅ b ⋅ b ⋅ b 10a²b² = 2 ⋅ 5 ⋅ a ⋅ a ⋅ b ⋅ b Identify the common factors in both monomials. These are the factors that appear in both factorizations with the same or lower exponent. The common factors are: 2, a, and b² Multiply the common factors to get the GCF. GCF = 2 ⋅ a ⋅ b² = 2ab²
The GCF is 3x3y2.
Monomial. Monomial. Monomial. Monomial.
It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial).
Monomial.
When you simplify each of those expressions you get 120xy, 210xy and 216xy. The GCF of those is 6xy because it divides evenly into all of them.
12ab