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Help with finding the GCF-Greatest Common Factor

Good afternoon,

I have just finished a lesson in Fractions that involves finding the GCF(Greatest Common Factor) of two numbers. It is important that the student has mastered his/her multiplication facts.If the student is struggling then they can use a multiplication chart. Using the chart repeatedly, will usually reinforce learning. I have provided an example:

FYI...
Product= the answer when two factors are multiplied together
Factors= two numbers multiplied together
When finding factors it is not necessary to repeat numbers such as;
in the factors of 4
they are: 1x4,4x1, and 2x2
It is only necessary to write each number once. {1,2,4}

Now let's try this!

Find the GCF of 4 and 10:
first write down all factors of 4; like 1x4, 4x1, and 2x2
the factors are {1,2,4}
next write down all factors of 10; like 1x10, 10x1,2x5, and 5x2
the factors are {,1,2,5,10}
Identify common factors of both 4 and 10; they are {,1,2}
Identify the largest or greatest factor; {2}
GCF= 2

Comments

Why not just use the Euclidean Algorithm?