Free Algebra Tutorials!
 Home Miscellaneous Equations Operations with Fractions Undefined Rational Expressions Inequalities Writing Equations for Lines Using Sequences Intersections of Lines and Conics Graphing Linear Equations Solving Equations with Log Terms and Other Terms Quadratic Expresions - Complete Squares Adding and Subtracting Fractions with Like Denominators Multiplying a Fraction by a Whole Number Solving Equations with Log Terms and Other Terms Solving Quadratic Equations by Factoring Locating the Solutions of the Quadratic Equation Properties of Exponents Solving Equations with Log Terms on Each Side http: Graphs of Trigonometric Functions Estimating Products and Quotients of Mixed Numbers Inequalities The circle Adding Polynomials Adding Fractions with Unlike Denominators Factoring Polynomials Linear Equations Powers of Ten Straight Lines Dividing With Fractions Multiplication Property of Equality Rationalizing Denominators Multiplying And Dividing Fractions Distance Between Points on a Number Line Solving Proportions Using Cross Multiplication Using the Quadratic Formula Scientific Notation Imaginary Numbers Values of Symbols for Which Fractions are Undefined Graphing Equations in Three Variables Writing Fractions as Decimals Solving an Equation with Two Radical Terms Solving Linear Systems of Equations by Elimination Factoring Trinomials Positive Rational Exponents Adding and Subtracting Fractions Negative Integer Exponents Rise and Run Brackets Multiplying Square Roots Multiplying Polynomials Solving Systems of Linear Inequalities Multiplication Property of Radicals A Quadratic within a Quadratic Graphing a Linear Equation Calculations with Hundreds and Thousands Multiplication Property of Square and Cube  Roots Solving Equations with One Log Term The Cartesian Coordinate Plane Equivalent Fractions Adding and Subtracting Square Roots Solving Systems of Equations Exponent Laws Solving Quadratic Equations Factoring Trinomials Solving a System of Three Linear Equations by Elimination Factoring Expressions Adding and Subtracting Fractions The parabola Computations with Scientific Notation Quadratic Equations Finding the Greatest Common Factor Introduction to Fractions Simplifying Radical Expressions Containing One Term Polynomial Equations Graphing and Intercepts The Number Line Adding and Subtracting Rational Expressions with Different Denominators Scientific Notation vs Standard Notation Powers Factoring by Grouping Extraneous Roots Variables and Expressions Linera Equations Integers and Substitutions Squares and Square Roots Adding and Subtracting Rational Expressions with Different Denominators Solving Linear Inequalities Expansion of a Product of Binomials Powers and Exponents Finding The Greatest Common Factor Quadratic Functions The Intercepts of a Parabola Solving Equations Containing Rational Expressions http: Subtracting Polynomials Solving Equations Adding Fractions with Unlike Denominators Solving Systems of Equations by Substitution Solving Equations Product and Quotient of Functions
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Finding the Greatest Common Factor (GCF)

After studying this lesson, you will be able to:

• Find the prime factorization of an integer.
• Find the GCF for a set of monomials.

Prime numbers are those numbers greater than one whose only factors are one and itself. A partial list of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...

One way to find a prime factorization of an integer is to use "factor trees".

Example 1

Find the prime factorization of 15

Factor the number down until all you have left is prime numbers

Write the prime factorization: 3 Â· 5

Example 2

Find the prime factorization of 30

Factor the number down until all you have left is prime numbers

Write the prime factorization: 2 Â· 3 Â· 5

Example 3

Find the prime factorization of -525

Factor out the negative to begin with

Write the prime factorization: -1 Â· 3 Â· 5 2Â· 7

Example 4

Find the prime factorization of 20a 2 b

Don't worry about the variables until the last step.

Write the prime factorization: 2 2 Â· 5 Â· a Â· a Â· b (we factored the variables, too)

Example 5

Find the prime factorization of 60a 2 b 2

Don't worry about the variables until the last step.

Write the prime factorization: 2 2 Â· 3 Â· 5 Â· a Â· a Â· b Â· b

## Greatest Common Factors

Sometimes we need to be able to find the greatest common factor of a set of numbers. The greatest common, or GCF, is the largest number that will divide evenly into each of the numbers in a set.

Example 6

Find the GCF for the set of numbers: 10, 12, 20

The largest number that will go into each of these numbers is 2.

Example 7

Find the GCF for the set of numbers: 6, 18, 36

The largest number that will go into each of these numbers is 6.

Example 8

Find the GCF for the set of numbers: 4, 8, 10

The largest number that will go into each of these numbers is 2.

Example 9

Find the GCF for the set of numbers: 8a 2 b, 18a 2 b 2 c

The first thing we do is find the GCF for the coefficients - just like we've been doing. The largest number that will go into each of the coefficients is 2.

Since we have variables, we have to find their GCF also. For a variable to be included in the GCF, each term must have the variable. If the variable is in each term, we take the lowest exponent of the variable and include it in the GCF.

In this case, both terms have a and both terms have b . We will include a 2 because that is the lowest power of a . We will include b because that is the lowest power of b .

The GCF will be 2 a 2 b

Example 10

Find the GCF for the set of numbers: 3x 2 y, 12x 4 y 2, 9x 2 y

The first thing we do is find the GCF for the coefficients. The largest number that will go into each of the coefficients is 3.

Since we have variables, we have to find their GCF also. For a variable to be included in the GCF, each term must have the variable. If the variable is in each term, we take the lowest exponent of the variable and include it in the GCF.

In this case, both terms have x and both terms have y . We will include x 2 because that is the lowest power of x . We will include y because that is the lowest power of y .

The GCF will be 3x 2 y

 All Right Reserved. Copyright 2005-2018