Factors...Factors...Factors and Multiples!

Math 1510-
This week was a definite refresher of math from the past for me.  I surprised myself a bit with my ability to remember the acronyms that were discussed this week.

To begin with the basics:

                    

3 x 4 = 12
3 and 4 are both factors of 12
12 is a multiple of both 3 and 4.

*Greatest Common Factor(GCF)-the greatest natural # that is a factor of all #'s involved in the problem

*Least Common Multiple(LCM)-the smallest natural # that is a multiple of all #'s involved in the problem

*Greatest Common Divisor(GCD)-the greatest natural # is a divisor of all the #'s involved in the problem

 And then we added:

*Prime Factorization- finding which prime numbers multiply together to make the original number.

 What are the prime factors of 12 ?

It is best to start working from the smallest prime number, which is 2, so let's check:

12 ÷ 2 = 6

Yes, it divided evenly by 2. We have taken the first step!
But 6 is not a prime number, so we need to go further. Let's try 2 again:

6 ÷ 2 = 3

Yes, that worked also. And 3 is a prime number, so we have the answer:

12 = 2 × 2 × 3

As you can see, every factor is a prime number, so the answer must be right.

Note: 12 = 2 × 2 × 3 can also be written using exponents as 12 = 2² × 3

Reminder:

Prime number-a natural # that has exactly two distinct factors, and is greater than 1

Composite number-a natural # that has more than two distinct factors

 

 My favorite part of this weeks lesson was learning to find the GCF of a number using the Euclidean Algorithm. 

 

                 I found this method to be very simple to use and it was fun to learn (and understand!) something new.