The GCF is the Greatest Common Factor, which means that it is the highest number that divides exactly into two (or more) numbers, in this case 55 and 100. You start off by listing all of the factors of both numbers. When you have finished, you find the highest factor that goes into them both, and that is the answer.
1, 5, 11, 55.
1, 2, 4, 5, 10, 20, 25, 50, 100.
As you can see, the highest number that goes into them both is 5. Therefore, the GCF of 55 and 100 is 5.