4.1+Greatest+Common+Factor

Section 4.1 - Greatest Common Factor
Recall from earlier that a factor was a number that could evenly "go into" another number. Factors of 15 are 1, 3, 5, and 15, because each of those divides evenly into 15.

Common factors suggest that you have two numbers, and you are trying to find factors that evenly go into both of them.

Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Common factors of 18 and 24: 1, 2, 3, 6


 * Greatest Common Factor ** means the biggest factor that a pair of numbers have in common. In the example above, 6 is the greatest common factor of 18 and 24.

So what? It will be very handy when you are reducing fractions or finding equivalent fractions in this chapter. There are also a few places later on where this will be valuable.

There are a few ways to find the greatest common factor shared by two numbers.

__Method 1__: Just like we did in the example, write out the factors and look for the biggest number that appears in both lists. This method is very tedious if the numbers are large.

__Method 2__: Do prime factorization for both numbers. When you finish, find the factors that are the same in both lists. Multiply those common factors and that will be the greatest common factor.

__Method 3__: Repeated division. Write both numbers and see if there is a factor that can be divided out of both. Divide it out, but write down the factor. Keep doing that until there are no more factors that evenly go into both numbers. Multiply all of the factors that did and that will be the greatest common factor.




 * Relatively Prime**

If two numbers share no factors except 1, they are considered to be "relatively prime". That doesn't mean that either number is a prime number, just that, relative to each other, there are no other factors but 1. An example would be 15 and 32 - neither is a prime number, but they share no common factors (except 1).


 * Factors with Variables**

Although you can't add or subtract unlike terms, such as constants and variables, you can multiply them. Those are factors being multiplied together, so the factors of 3B are 3 and B. The common factors of 34ABC and 24AC are 1, 2, A, and C.


 * Chapter Four Practice Problems**

**Where to from here?**
4.1 Greatest Common Factor 4.2 What is a Fraction? 4.3 Equivalent Fractions 4.4 Multiplying Fractions 4.5 Dividing Fractions 4.6 Adding and Subtracting Like Fractions 4.7 Adding and Subtracting Unlike Fractions 4.8 Fraction Coefficients 4.9 Solving for X with Fractions Chapter Four Review Chapter Four Homework