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Lesson 2 — Activity 2: Greatest Common Factor (GCF)
Completion requirements
Lesson 2 — Activity 2: Greatest Common Factor (GCF)
Getting Ready
Now that you have done some work on multiples of numbers, you will work on factors of numbers.
The factors of a number are all those numbers that can divide evenly into the number with no remainder. This will include the number itself and
1.
For example, let's look at the number 10 and list all the numbers that will divide evenly into it. We'll start with 2 and continue from there. (Remember, 10 and 1 will be on our list.)
You will know when all the factors have been found when you divide by a number that you already have as a factor, or when you get the same number as the number you are dividing by. Each factor should only be listed once.
 10 ÷ 1 = 10
 10 ÷ 2 = 5
 10 ÷ 3 = does not divide evenly, decimal number
 10 ÷ 4 = does not divide evenly, decimal number
 10 ÷ 5 = 2
We can stop as we have divided by a number we already have as a factor, in this case, 5.
The set of factors of 10 is:
10: {1, 2, 5,10}
Try This:
Use the number 12.
Can you list all the numbers that divide evenly into it?
Try starting with 2 and continue from there. (Remember 12 and 1 will be on your list.)

12 ÷ 1 = 12

12 ÷ 2 = 6

12 ÷ 3 = 4

12 ÷ 4 = 3

12 ÷ 5 = does not divide evenly, decimal number

12 ÷ 6 = 2
You can stop as you have divided by a number you already have as a factor, in this case, 6.
The set of factors of 12 is:
12: {1, 2, 3,4, 6, 12}
Now think about this situation:
You decide to have a few friends over to watch a movie. You have 24 tarts for snacks and 18 cans of fruit juice.
You need to know how many people you can invite if you want each person to get the same amount of snacks. In order to do this, you have to find the largest number that evenly goes into both numbers. We call this number the greatest common factor (GCF).
To find the GCF, you must list all of the numbers that go into each number (the factors) and then find the largest common number on both lists.
Let's list the factors for the number 24 first.24 ÷ 1 = 24 (1 and 24 are factors of 24)24 ÷ 2 = 12 (2 and 12 are factors of 24)24 ÷ 3 = 8 (3 and 8 are factors of 24)24 ÷ 4 = 6 (4 and 6 are factors of 24)24 ÷ 5 = 4.8 (Answer is a decimal number, so 5 is not a factor of 24)24 ÷ 6 = 4 (You can stop now as you already know 6 is a factor of 24.) 
Now let's list the factors for the number 18.18 ÷ 1 = 18 (1 and 18 are factors of 18)18 ÷ 2 = 9 (2 and 9 are factors of 18)18 ÷ 3 = 6 (3 and 6 are factors of 18)18 ÷ 4 = 4.5 (Answer is a decimal number, so 4 is not a factor of 18)18 ÷ 5 = 3.6 (Answer is a decimal number, so 5 is not a factor of 18)18 ÷ 6 = 3 (You can stop now as you already know 6 is a factor of 18.) 
The set of factors of a number are listed in order from LEAST to GREATEST and separated by commas.
The set of factors of a number are listed in order from LEAST to GREATEST and separated by commas.
The set of factors of 24 is: 24: {1, 2, 3, 4, 6, 8, 12, 24}
The set of factors of 18 is: 18: {1, 2, 3, 6, 9, 18}
Compare the two lists and find the largest number. This will be the greatest common factor of 24 and 18. That number is 6.
So you know that you can invite six friends over for movie night. Divide the number of tarts and juice boxes by 6.
 24 tarts ÷ 6 = 4 tarts each
 18 juice boxes ÷ 6 = 3 juice boxes each
Try This:
At the beginning of the activity, you listed the factors for the number 12.
Remember that they were:
12: {1, 2, 3, 4, 6, 12}
Now, list the factors for the number 16. Then, determine the greatest common factor of 12 and 16.
16:
 16 ÷ 1 = 16 (1 and 16 are factors of 16)

16 ÷ 2 = 8 (2 and 8 are factors of 16)

16 ÷ 3 = 5.3 (Answer is a decimal number, so 5 is not a factor of 24)

16 ÷ 4 = 4 (You can stop as you got the same number as the number you were dividing by; 4 is a factor of 16)