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Q: Can a greatest common factor have a variable with an exponent?

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There is no Greatest Common Factor (GCF) for a single number. The Greatest Common Factor (GCF) is the largest factor common to two or more given numbers.

You look at the exponents. x5y2 and x3y4 The greatest common factor of these is the largest exponent of each. So the greatest common factor is: x3y2

The GCF of 102 and 104 is 102

The GCF is 15x^3.

The base is the common factor multiplied repeatedly by the exponent.

First.. find the gcf of the coefficients.Second.. remember the word 'common' .. for the variables only variables that appear in all the monomials are common factors, look at the exponents of that common variable, use the smallest exponent for that variable.Third.. Put them all together.. that is the gcf.EX: Find the gcf for 15x2y6 and 12x3yzThe gcf of the coefficients, 15 and 12, is 3.x is a common variable ... its smallest exponent is 2 .... x2y is a common variable ... its smallest exponent is an understood 1 ... ynote that z is NOT a common variableSo the GCF is 3x2y

The GCF is 5.

Just choose the smaller exponent. The GCF of a3 and a5 is a3

For the greatest common factor, you check which variables appear in each of the expressions. In the case of exponents, you take the lowest exponent for each variable. For the least common multiple, you take each variable, whether it appears in all of the expressions involved, or only in some of them. In the case of the exponents, you take the greatest exponent for each variable. If there are numeric coefficients (numbers as products), you take either the gcf or the lcm of those in the usual way.

A variable can be any number. The GCF possibilities are infinite.

A variable can be any number. The GCF possibilities are infinite.

Simplification using the greatest common factor does.Simplification using the greatest common factor does.Simplification using the greatest common factor does.Simplification using the greatest common factor does.

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