Question

find the greatest common factor of the following monomials

Answer 1

Answer:

The greatest common factor is: 2a²b⁴.

Step-by-step explanation:

Given: 32a⁶b⁵ & 26a²b⁴

32a⁶b⁵ = 2 x 2 x 2 x 2 x 2 x a x a x a x a x a x a x b x b x b x b x b

26a²b⁴ = 2 x 13 x a x a x b x b x b x b

Hence the common factors are: 2 x a x a x b x  b x b x b

Therefore, the GCD is: 2a²b⁴

Hence, the answer.

Answer 2

Start by finding the greatest common factor of 32 and 26.

You can do this a few different ways, but I will be listing the multiples

of each number and then finding the largest factored shared.

However, if you prefer doing a factor tree or another method,

that is totally fine and feel free to do that.

Let's first divide 36 by 1 and go on.

36 ÷ 1 = 36

36 ÷ 2 = 18

36 ÷ 3 = 12

36 ÷ 4 = 9

36 ÷ 6 = 6

All the numbers in bold are factors of 36.

So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Now let's find the factors of 26.

Let's first divide 26 by 1 and go on.

26 ÷ 1 = 26

26 ÷ 2 = 13

All the numbers in bold are factors of 26.

So the factors of 26 are 1, 2, 13, and 26.

The largest factored shared by the two lists is 2.

So 2 is the greatest common factor of 32 and 26.

Now let's look at the variables.

The variable must appear in both monomials

in order for it to qualify for the greatest common factor.

In this case, a and b are in both so they will both qualify.

For the greatest common factor, we will use

the smallest power on each of the variables.

Since we have an a⁶ and an a², we will use a²

for the greatest common factor.

Since we have a b⁵ and a b⁴, we will use b⁴

as the greatest common factor.

So our answer is 2a²b⁴.