Finding the Greatest Common Factor (GCF)
The greatest common factor (GCF) of a set of terms is the largest expression that divides each term without leaving a remainder. To find the GCF of the terms 60x4y7, 45x5y5, and 75x3y, we need to follow these steps:
Step 1: Factor the coefficients
First, look at the numerical coefficients of each term:
- 60 = 2 × 2 × 3 × 5
- 45 = 3 × 3 × 5
- 75 = 3 × 5 × 5
Step 2: Identify the common factors
The prime factors common to all three coefficients are:
- 3
- 5
Now, multiply these common factors:
3 × 5 = 15
Step 3: Factor the variables
Next, we will look at the variable parts:
- x4
- x5
- x3
For the variable x, the lowest power is x3.
- y7
- y5
- y1
For the variable y, the lowest power is y1.
Step 4: Combine the GCF components
Now, combine the GCF of the coefficients with the GCF of the variables:
GCF = 15x3y1
Final Result
Thus, the greatest common factor of 60x4y7, 45x5y5, and 75x3y is:
15x3y