An often used way to search for common factors is a T-Chart. Here is how you get started.
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Lets take 30 as an example . First , you list 30 at the top of the T-Chart. Second, start finding the factors of 30. We know that one goes into every number as a factor, so 1 and 30 are factor pairs. Third, the second number that goes into 30 is 2 because 2x15 is 30. We know 2 works because 30 is even. Fourth, the next number that goes into thirty is 3 because 3 x 10= 30 because 10 x anything equals that number with a zero on the end. Fifth, 4 won't go into 30 so you cant use 4. 4 times 7 is 28 and 4 times 8 is 32. Seventh, 5 goes into thirty 6 times. We knew 5 would work because the number ends in a zero. Finally, we can tell we are done because when we try 6 the numbers cross over. ln thirties T-chart 5 x 6= 30 and 6 x 5=30 too. Because they cross over that tells you that you have found all the factors of 30.
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Here is another example of a T-chart using the number 20.

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