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Ahhh, how to teach GCF in third grade? 
Just tell them what you have learned and don't be afraid to express your ideas!
You: What is the GCF of 18 and 12?
First, what is the meaning of GCF?
Student: What?
You: It means Greatest Common Factor
Student: Ahhhhh! What is that?
You: Here, factors are numbers that can divide a number. Example, 2 is a factor of 18 because it can divide 18 by 2 and gives 9 that is a whole number. (Give them exercises about factors)
You: Now, to answer the question I gave earlier, first, let us list all the factors of the given numbers.
18= 1, 2, 3, 6, 9, and 18
12= 1, 2, 3, 4, 6, and 12
You: What numbers are common among them? (Answer: 1, 2, 3, and 6)
They are what we called as common factors! But, we are asked about the GREATEST COMMON FACTOR. So, which of them is the greatest? (Answer: 6)
So the GCF of 12 and 18 is 6! Got it! Very good!
(You can make your own style! It would be better if you make it yourself! and make sure that your students are listening to you!)(Be careful because 3rd graders are different and they may have some problems! Good luck!)