Preparation 
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How to Find the GCF in Two or More Algebraic Terms ?
Finding the Greatest Common Factor (GCF) in two or more algebraic terms involves three steps:
1. Find the GCF of all the coefficients (numbers).
2. Find the GCF of all the variables (letters) by taking each variable to its lowest exponent.
3. Write the GCF of the terms as the product of the GCF of the coefficients and the GCF of the variables.
Example 1. GCF of 8x^{4}, 4x^{2} and 12x is 4x.
Here, the GCF of the coefficients (8, 4 and 12) is 4.
The GCF of the variables (x^{4}, x^{2} and x) is x (i.e., the variable raised to the lowest exponent).
The GCF of the terms 8x^{4}, 4x^{2} and 12x is 4x (i.e., the product of 4 and x).
Example 2. GCF of 27ab^{3} and 18a^{2}b^{2} is 9ab^{2}.
Here, the GCF of the coefficients (27 and 18) is 9.
The GCF of the variables (ab^{3} and a^{2}b^{2}) is ab^{2} (i.e., each variable with its lowest exponent).
The GCF of the terms 27ab^{3} and 18a^{2}b^{2} is 9ab^{2} (i.e., the product of 9 and ab^{2}).
Note that a variable having an exponent of one is written without an exponent (i.e., x^{1} = x) and a variable with an exponent of zero equals one (i.e., x^{0} = 1).
Practice Exercise for Algebra Module on Finding GCF in Algebraic Terms
