If the want to find the greatest common factor of the numbers,
12 and 16, you would have the kids draw their "party" tables. The play on the word tables helps us left-brained people. Just have them always number the left side of each table 1-8.
Factors are the two numbers that are multiplied together to make another number. In the table on the left 1 x 12 =12, 2 x 6 = 12, 3 x 4= 12, 4 x3=12, 5 is not a factor of 12, and 6 x 2=12.
The table on the right factors the number 16 in the same way.
Then I ask the kids if there is a number that is the same in each table. The number in common to both tables is 4. Because we are starting with the 12 and 16, and doing the tables in this manner, the number in common will be the GCF.
After we did several of these, I could see the lightbulbs going off in a lot of their heads.
I have been doing these tables in Algebra (see Who Let The Dogs Out post), so you know that this is going to be a very handy tool for math here.