To find the greatest common factor (GCF) of the expressions 20x4 and 6x3, we follow a systematic approach involving both the numerical coefficients and the variable components.
Step 1: Find the GCF of the numerical coefficients
The numerical coefficients here are 20 and 6. We start by determining the factors of each number:
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 6: 1, 2, 3, 6
The common factors of 20 and 6 are 1 and 2. The greatest of these is 2.
Step 2: Find the GCF of the variable components
For the variable part, we have x4 and x3. The GCF of the variables is determined by taking the lowest exponent of the variable that appears in both terms. Here, the lowest exponent of x is 3.
Step 3: Combine the GCFs
Now, we combine the GCFs we found:
- From the numerical coefficients, we have 2.
- From the variable components, we have x3.
Therefore, the greatest common factor of 20x4 and 6x3 is:
2x3
This means that 2x3 is the highest factor that divides both 20x4 and 6x3 without leaving a remainder.