The factors of a number are all of the positive whole numbers that go into it evenly. For example, 2 is a factor of 6 because 6 ÷ 2 = 3, or equivalently, 6 = 2 x 3. Note that this naturally implies that every whole number has 1 and itself as a factor.
The numbers that go evenly into 24 are 1, 2, 3, 4, 6, 8, 12, and 24. For 27, those numbers are 1, 3, 9, and 27.
The common factors between two numbers are numbers that go into both numbers evenly. Looking through the lists for 24 and 27, we see that 1 and 3 are their common factors. The greatest common factor is, of course, the largest of these, so the greatest common factor of 24 and 27 is 3.
