Find the GCF of 45g + 30h
To find the greatest common factor (GCF) of 45g + 30h, we need to determine the highest common factor that can be factored out from both terms.
First, let's factor out the numerical coefficients 45 and 30:
45 = 3 * 3 * 5
30 = 2 * 3 * 5
Now, let's look at the variables g and h. The term with the lowest exponent for each variable is g, which has an exponent of 1. The term with the lowest exponent for h is h itself, which also has an exponent of 1.
Since there is no other common factor between the terms (such as variables or exponents), the GCF of 45g + 30h is just the product of the common factors of the numerical coefficients, which is:
GCF(45g + 30h) = 3 * 5 = 15
Therefore, the GCF of 45g + 30h is 15.
Factor 9z + 18 using the GCF
To factor 9z + 18 using the greatest common factor (GCF), we first need to determine the GCF of the two terms.
Let's factor out the numerical coefficients 9 and 18:
9 = 3 * 3
18 = 2 * 3 * 3
The common factor between the two terms is 3.
Next, let's consider the variable z. Both terms have a z, so we can factor out z as well.
Putting it all together, we have:
9z + 18 = (3 * 3 * z) + (2 * 3 * 3)
= 3z(3 + 2 * 3)
Simplifying further:
9z + 18 = 3z(3 + 6)
= 3z(9)
Therefore, the factorization of 9z + 18 using the GCF is 3z(9).
To find the greatest common factor (GCF) of 45g and 30h, we need to factor both terms.
First, let's factor 45g:
45 is divisible by 5, so we can write 45 as 5 * 9.
g is a prime variable, so there's nothing further we can factor.
Now, let's factor 30h:
30 is divisible by 2 and 3, so we can write 30 as 2 * 3 * 5.
h is a prime variable, so there's nothing further we can factor.
Next, we can determine the common factors between 45g and 30h:
Both terms have a factor of 5.
Both terms have a factor of 3.
Taking the common factors into account, the GCF of 45g and 30h is 5 * 3, which is equal to 15.
To find the greatest common factor (GCF) of the terms 45g and 30h, we need to determine the largest number or variable that can divide both terms evenly.
Step 1: Factorize the coefficients:
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Step 2: Identify the common factors:
The common factors of 45 and 30 are 1, 3, 5, and 15.
Step 3: Identify the greatest common factor:
The greatest common factor of 45 and 30 is 15.
Step 4: Identify the common variables:
In this case, the variables are g and h. Since they are different variables, they do not have any common factors.
Therefore, the greatest common factor (GCF) of 45g and 30h is 15.