How do you find the greatest common factor of #30y^3, 20y^2#?

Answer 1

#10y^2#

Find the greatest common factor (GCF) of #30y^3# and #20y^2#.
First, let's find the GCF of the coefficients #30# and #20# by listing their factors.
#30#: #1, 2, 3, 5, 6, 10, 15, 30#
#20#: #1, 2, 4, 5, 10, 20#
The greatest factor that is "common" to both lists is #10#. In other words, the largest number that can "go into" both #30# and #20# without a remainder is 10.

Now, let's find the GCF of the variables.

#y^3= y *y*ycolor(white)(aaa)y^2=y*y#
The largest number of "#y#"'s common to both #y^3# and #y^2# is #y*y#.
The GCF of the variables is #y^2#.
Combing the the GCF's of the coefficients and the variables gives a GCF of #10y^2#.
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Answer 2

To find the greatest common factor of (30y^3) and (20y^2), we identify the highest power of each common factor.

The prime factorization of 30 is (2 \times 3 \times 5), and for 20, it is (2 \times 2 \times 5). So, the greatest common factor of the coefficients is (2 \times 5 = 10).

For the variables, (y^3) and (y^2) both have (y) as a common factor, and the greatest power of (y) in both terms is (y^2).

Therefore, the greatest common factor of (30y^3) and (20y^2) is (10y^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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