I am having trouble finding the greatest common factor when there is a variable. I have these two problems I need help with.
1. what is the GCF of 7x^2 and 14x^3
2. what is the GCF of 4x^5 and 6x^7
The exponents are throwing me off.
http://www.math.com/school/subject1/lessons/S1U3L2GL.html
The first is 7x^2 ...it divides into each.
To find the greatest common factor (GCF) when there is a variable involved, you can use the following steps:
Step 1: Identify the common factors of the coefficients. In the first problem, the coefficients are 7 and 14, so the common factor is 7. In the second problem, the coefficients are 4 and 6, so the common factor is 2.
Step 2: Identify the common factors of the variables. In both problems, the variable is x. In the first problem, the variable has an exponent of 2, and in the second problem, the variable has exponents of 5 and 7. The lowest exponent value is 2 in the first problem, and 5 in the second problem.
Step 3: Combine the common factors. In the first problem, the common factor is 7 and x^2. So the GCF is 7x^2. In the second problem, the common factor is 2 and x^5. So the GCF is 2x^5.
If you want to validate your answer or find the GCF for more complicated expressions, you can use an online calculator or refer to resources like the one you mentioned: http://www.math.com/school/subject1/lessons/S1U3L2GL.html.
Remember that when finding the GCF, you are looking for the greatest factor that divides into both terms. In these examples, 7x^2 is the largest expression that can divide into both 7x^2 and 14x^3, and 2x^5 is the largest expression that can divide into both 4x^5 and 6x^7.