Number theory and prime factorization -1510

Wow! I have actually enjoyed this topic! I find it fun to draw a factor tree and bring it all down to the lowest low. I found a nice little game at STUDYJAMS that tests your knowledge of prime factorization. What is nice about this site is the tutorial section or Step by Step area that explains the process. I can see using this site in class to supplement the topic. In our district we have a wonderful teacher in 3rd grade who really uses his classroom homepage to offer on-line resources to help his math students to practice their skills at home. Other teachers often link to his classroom page since he's done a great job of finding things like this. I certainly envision using the Internet to connect students with school when they are home and StudyJams would make my list.

The Sieve of Eratosthenes is a great way to help students determine the prime numbers between 1 and 100. Basically, you find a prime number...say 2 and then remove all multiples of 2 like water from spaghetti and move on to the next prime number...3;remove its multiples and so on. Once all the composite numbers have been drained away you are left with nothing but prime noodles numbers. Who was this Eratosthenes? Well, he was a Greek mathematician from long, long ago (say 276 BC to 195 BC) and from the looks of it,

he had a large noodle himself. Thanks to his technique we can use his sieve, or colander, to drain away composite numbers. Efxaristo, Eratosthenes!



The big question remains...what do I do with this prime factorization information? Say for instance you want to figure out the Greatest Common Factor of two numbers. Why would you want to do that? If you had two great big piles of things that needed to be grouped evenly for instance. Then using the prime factorization will entail comparing the two numbers prime factors and combining just those factors that show up in both. On the flip side you could use them to find the Lowest Common Multiple of two numbers (or more if you are so inclined). This would mean taking the factors common to both numbers raised to the highest power of that prime that happens in either number. Then multiply the prime factors out and Viola! You have found the Least Common Multiple. Which can be used to determine when two events might occur simultaneously.