Greatest Common Factor (GCF) Examples
This page will show problems on the greatest common factor with GCF examples.
To factor means to find two or more quantities whose product equals the original quantity.
GCF Quiz with Examples
Instructions: Try this GCF quiz, after studying the examples below. You need to find the greatest common factor of the following expressions.
[WpProQuiz 18] |
How to Find the Greatest Common Factor
The greatest common factor of two numbers in the largest number that is a factor of both of them.
Consider the following algebraic expression:
30x2y3z + 18x3y2z2 + 24xy4z3
To find the greatest common factor, we need to follow these steps:
STEP 1:
Look for the common variables and exponents.
Variables: Each term has a factor of x, a factor of y, and a factor of z.
Exponents of x: The exponents on the x variables of each term are 2, 3, and 1. The common factor will be the variable with the smallest exponent. So, x1, simplified to x, is a common factor.
Exponents of y: The exponents on the y variables of each term are 3, 2, and 4. Remember that the common factor will be the variable with the smallest exponent. So, y2 is a common factor.
Variable z: The exponents on the z variables of each term are 1, 2, and 3. So, z is a common factor.
GCF for variables: Accordingly, the common factor for the variables is xy2z.
STEP 2:
Look at the coefficients. Remember that a coefficient is the number part of the term.
Our equation is: 30x2y3z + 18x3y2z2 + 24xy4z3
Coefficients: The coefficients are 30, 18, and 24. We need to find the greatest common factor for the coefficient part of the expression.
Dividing: To do this we have to find the largest number that each of these numbers (30, 18, and 24) can be divided by.
List the Common Factors: Each of these coefficients can be divided by 6. So each coefficient has a factor 6. There is no larger common factor.
30 = 6 × 5
18 = 6 × 3
24 = 6 × 4
STEP 3:
The common factor for the variables is xy2z and the common factor for the coefficients is 6.
Final GCF: The greatest common factor is 6xy2z.
STEP 4:
Re-write the expression in factored form, placing the GCF at the front of the new expression.
Work out the expression:
30x2y3z + 18x3y2z2 + 24xy4z3 =
(6 × 5)(x × x)(y2 × y)z + (6 × 3)(x × x2)y2(z × z) + (6 × 4)x(y2 × y2)(z × z2) =
6xy2z(6 × 5)(x × x)(y2 × y)z + (6 × 3)(x × x2)y2(z × z) + (6 × 4)x(y2 × y2)(z × z2) =
6xy2z(5 × x × y) + (3 × x × z) + (4 × y2 × z2) =
Factored Expression: 6xy2z(5xy + 3xz + 4y2z2)
Factoring – Further Practice
Before you go on to other topics, you should look at the following post:
Try our free algebra practice test
