We can factor each of the given terms so that 4x^2 shows up
8x^5 = 4x^2*2x^3
12x^3 = 4x^2*3x
20x^2 = 4x^2*5
This shows how 4x^2 is the GCF of 8x^5, 12x^3, and 20x^2
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Here's how to find the GCF of terms involving variables.
First, find the GCF of the coefficients 8, 12 and 20.
List the prime factorizations
- 8 = 2*2*2
- 12 = 2*2*3
- 20 = 2*2*5
Then circle "2*2" since it is found in all three factorizations. Do not circle 3 because it's not found in 8 or 20. Do not circle 5 since it's not found in 8 or 12.
Therefore, the GCF of {8,12,20} is 2*2 = 4.
As for the variable terms, we look for the smallest exponent.
The exponents for x^5, x^3, x^2 are 5,3,2 in that order. The smallest exponent is 2, so x^2 is part of the GCF.
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Summary:
We found the GCF of the coefficients was 4.
The GCF of the variable terms was x^2
That's how we arrive at the GCF of 4x^2