Question

Find the greatest common factor of the following monomials:
26ab^4, 13a²b^6

Answer 1

To find the greatest common factor (GCF) of the monomials 26ab^4 and 13a²b^6, we need to identify the highest power of each variable that appears in both monomials. The GCF of 26ab^4 and 13a²b^6 is ab^4.

Step-by-step explanation:

To find the greatest common factor (GCF) of the monomials 26ab^4 and 13a²b^6, we need to identify the highest power of each variable that appears in both monomials. In this case, the variables are a and b.

Let's look at the powers of a first. Both monomials have a to the power of 1, so the highest power of a that appears in both monomials is 1.

Now let's look at the powers of b. The first monomial has b to the power of 4, and the second monomial has b to the power of 6.

Since 4 is smaller than 6, the highest power of b that appears in both monomials is 4. Therefore, the GCF of 26ab^4 and 13a²b^6 is a^1b^4, which can be written as ab^4.