# Greatest Common Factor (GCF) – Least Common Multiple (LCM)

In order to find the greatest common factor of two numbers, you need to list all the factors of each number and choose the greatest one even if the number is one of the two numbers.

• The greatest common factor of 35 and 280 is:
(A) 5
(B) 7
(C) 35
(D) 70
(E) 280

There is another way to find the GCF i.e. use the prime factorization tree. For prime factorization tree, simply break each number down to its prime numbers. Encircle those numbers they have in common and multiply them.

• What is the GCF of 425 and 1020?

425 and 1020 have one 5 and one 17 in common.  Hence, the GCF is 85.

In order to find Lowest Common Multiple, the most accurate and easy way is also to use the prime factorization tree. But for this, you will keep only one of each number that they have in common and then multiple those numbers by all the prime factors that are leftover. Let’s take the example of 425 and 1020 again. We will keep one 5 and one 17. Now cross off the 5 and 17 listed under 1020 so you don’t multiply them by mistake. And then use the leftovers. We will have 5 times 5 times 17 times 2 times 2 times 3. Hence, the LCM of 425 and 1020 is 5100.