Factors! Factors! Factors!
Factor: A number that is divisible by another number evenly, or with out anything left over.
How do you solve a factor? Thinking this? Well, don't worry I'm here to help you!
Ex. List the factors of 24.
Step 1: You need to know that the number 1 and the number you're trying to find the factors for ( In this case 1 and 24) can always go into the number (In this example 24) evenly. So there you have it your first factor pair!
Wait! you might be thinking. What is a factor pair. Well let me explain it to you in non-mathematical terms. A Factor pair is the two numbers (factors) that add up to your main number. (In our example up above, the pair we already have is 1 and 24 because 1*24=24).
Step 2: Now that you know what a factor pair is you are ready to move on. Step two is to find if there are any other numbers (factors) that can go evenly into your number.(Since our example is 24, let's try 2. 24/2=12. So, 2 is a factor of 24. But wait! You have to make it a factor pair. In this case the factor pair would be 2 and 12. Still not sure why? Well, it's simple because 12*2=24. It goes in evenly).
Step 3: It is basically step 2. You just have to keep testing numbers (under 24 of course) to see if they go in evenly until you have all the pairs. (I'm going to tell you all the other factor pairs of 24: 3 and 8 and 6 and 4).
Hold on a second. Your saying I have to test ALL the numbers from 1 to 24 to see if they go in evenly that will take all day.
I have an answer to that complaint and surprisingly it's no. You do not have to test ALL the numbers. There are a couple tricks. For one if you test 24/2=12 then you know you don't have to test the 12 because you all ready know it goes in evenly. The second trick (if we are still using 24 as are example) is say you were testing five. You know that 5*5=25. That's over 24. So that means that you don't have to test anymore numbers over 5 (in this case) assuming you did the numbers in factor pairs first.
GCF!
What does GCF stand for? I'll tell you. GCF stands for Greatest Common Factor.
Greatest Common Factor: The Greatest factor that can go evenly into two numbers.
How do I find the GCF? Your probably wondering this, too. Well, guess what, I'll tell you this, too. So, stay in your chair and read on.
Ex. Find the GCF of 12 and 16.
Step 1: List the factors of your first number. (In this case it is 12. So the factors of 12 are: 1 and 12, 2 and 6, and 3 and 4).
Step 2: List the factors of your second number. (In this case the number is 16. So the factors of 16 are: 1 and 16, 2 and 8, and 4 and 4.
Step 3: Look at your two lists of factors. Find the numbers that are factors of both numbers. They will appear in both sets. (In this case the numbers are 1, 2, and 4).
Step 4: Look at the the new list (the list of factors) that you just made. Find the biggest number in the group. (Ours is 4).
Step 5: That's your GCF! (Once again, ours is 4).
When will I need to know this? Well, you need to know how to do these procedures to simplify fractions. If you didn't know how to find the GCF you could end up dividing for hours. (Boring!)
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