More Fun (Thanks Mrs. Schwartz)

Just for Fun!

Why Prime Factorization Matters

The following video gives you a preview of some of the work we will be doing in the next unit. I briefly demonstrated how you could use prime factorization to reduce fractions to a couple of the classes. I will go into more detail about this in the future. But for now, this video is a great explanation and demonstrates the power of prime factorization.

Explanation of prime factorization

The following video is a good review of prime factorization.  Prime factorizations is possible because of the Fundamental Theorem of Arithmetic.  Think about what the word fundamental means.  It means the basis of something.  Therefore the Fundamental Theorem describes the basis of numbers which are products of their prime factors and therefore unique!

A little inspiration..

More GCF & LCM Word Problem Guidance (Cobb County School District

Finding LCM Using Prime Factorization

Like GCF, you can use prime factorization to find the LCM of two or more numbers.  First find the GCF since the LCM and both numbers will share this factor.

Then multiply the GCF to all the remaining prime factors.  You are doing this because the prime factor string for the LCM must account for all the prime factors in your original numbers.  If not then you do not have the LCM.

Notice every prime in the prime factor string for the LCM (2160) is used at least once.  It is important to understand that the prime factor string for the LCM (2160 in this case) is the shortest factor string possible that will account for the prime factor strings of 144 and 1080.  This is the very meaning of least common multiple.  If you multiply the factor sting for 2160 by 2, you have a common multiple of 144 and 1080 but it is not the least common multiple.