For the past few days, in Math, we have been learning about prime factors, prime numbers, composite numbers, and many different ways we can deal with them. An example of ways we can deal with them is to find the greatest common factor between two or more numbers. By doing this, we can identify how multiple numbers relate with each other. Here are some examples of how to find the greatest common factor.
One quick, easy, and efficient way to find the Greatest Common Factor or GCF is to use prime factorization. Prime factorization is when we break down a divisible number until it is to its prime factors. Using this process, we can find the GCF by finding which prime factors between our numbers match and to multiply them together to find the number. We can use prime factorization using two main methods, Factor Trees and Division Tables.
For our first example we are going to find the GCF of numbers 150 and 420 using the Factor Tree. To use a factor tree, we write out our number, and find two factors, that make the number we are breaking down, a product. An example of this is we use 150, and two factors that form 150 as a product is 15 and 10. Then we break down those numbers into their factors which for 15 is 5 and 3 and 10 is 5 and 2. When we reach a number that cannot divide any further evenly, we have our number’s prime factors. On the left, we broke down 150 into its prime numbers which are 5, 5, 3, and 2. On the right , we also broke down 420 into its prime factors which are 2, 2, 3, 5, and 7. Next we identify which prime factors the two numbers have in common which are 2, 3, and 5 once each. Then we multiply them together to find the GCF which in this case is 30.
For our second example, we are choosing 483 and 575 and using the division table process. To use a division table, we write our number, and slowly divide the number, putting the divisor on the left of the dividend, and divide until our number becomes one. Essentially by doing this, we find the prime factors because they are the divisors on the left. On the left of the page, we divide 483 by 3 to make 161, then divide that by 7 to make 23, and finally divide 23 by itself to make 1. The numbers on the left of the dividend are the prime factors. We do the same thing for our right number and see which prime factors are in common. Then the process becomes the same as the factor tree, multiplying the common factors together and to get the GCF. In this case, the only common factor is 23 which is the greatest common factor.
Using these two ways of prime factorization makes it much easier to find numbers like the Greatest Common Factor and Lowest Common Multiple which is something a little different. It may see complicated above, but when you understand the concept, it makes it much easier to get our desired answer in prime factorization.