1.) Find the GCF of -25a3b4, 45a6b5.
I got 25a3b4
2.)Find the GCF of a5b, a3b4, a2b3.
I got a2b
3.) Find the GCF of 10ab5, 12a3b4, 16a2b3.
I got 2ab3
Please someone answer me
GCF of two numbers means that the GCF divides each of the two numbers.
1. 25a3b4 does not divide one of the two numbers, so it is not the GCF.
2. a²b is correct.
3. 2ab³ is correct.
Thanks!
You're welcome!
To find the greatest common factor (GCF) of two or more terms, we need to identify the highest power of each variable that is common to all terms.
1.) GCF of -25a3b4 and 45a6b5:
To find the GCF, we need to look at the factors of the coefficients and variables in both terms. For the coefficients, we have -25 and 45. The GCF of these numbers is 5 since 5 divides both -25 and 45.
Next, let's look at the variables. In both terms, we have 'a' raised to different powers (3 and 6) and 'b' raised to different powers (4 and 5). To find the highest power common to both terms, we take the minimum power of each variable. Thus, the highest power of 'a' that is common to both terms is 3, and the highest power of 'b' that is common to both terms is 4.
Therefore, the GCF of -25a3b4 and 45a6b5 is 5a3b4.
2.) GCF of a5b, a3b4, a2b3:
For this question, we need to find the GCF of three terms: a5b, a3b4, and a2b3.
Looking at the coefficients, we see that the GCF is 1 since all three terms have a coefficient of 1.
Next, let's examine the variables. We have 'a' raised to different powers (5, 3, and 2) and 'b' raised to different powers (1, 4, and 3). To find the highest power common to all three terms, we take the minimum power of each variable. Therefore, the highest power of 'a' that is common to all three terms is 2, and the highest power of 'b' that is common to all three terms is 1.
Hence, the GCF of a5b, a3b4, and a2b3 is a2b.
3.) GCF of 10ab5, 12a3b4, 16a2b3:
For this question, we need to find the GCF of 10ab5, 12a3b4, and 16a2b3.
As before, let's start with the coefficients. The GCF of 10, 12, and 16 is 2 since 2 divides all three numbers.
Then, looking at the variables, we have 'a' raised to different powers (1, 3, and 2) and 'b' raised to different powers (5, 4, and 3). The minimum power of 'a' is 1, and the minimum power of 'b' is 3.
Therefore, the GCF of 10ab5, 12a3b4, and 16a2b3 is 2ab3.