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Short answer: 2
Explanation: Let's factor out the smallest number first. The factors of 12 are 1,2,3,4,6, and 12. Now we'll take the largest of those factors and see if its a factor of the other two. 12 isn't a factor of either, so we'll look at the next biggest and work our way down. 6 is a factor of 18 but not 44 so that's out. 4 isn't a factor of 18. 3 isn't a factor of 44. 2 is a factor of both 18 and 44, so that is our greatest common factor.
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