During the first week of Foundations of Mathematics and Pre-Calculus 10, I learned how to use prime factorization to find the greatest common factor and the lowest common multiple. To find the GCF and the LCM, I used the tree diagram. The tree digram in my opinion is easier and better to use, rather than the division table. The greatest common factor of a set of numbers is the largest whole number which divides exactly into each of the members of the set. To determine the GCF, you need to find the product of each prime factor which is common to each prime factorization, then you multiply those factors that both numbers have in common. Next, to determine the LCM, take all the prime factors of one of the numbers and multiply by any additional factors in the other numbers. The larger the numbers are, the harder it is. Before, using this technique, you need to know how to do prime factorization initially. When you have larger numbers, sometimes using long division is required, although there are other techniques you can do.
