PRIME AND COMPOSITE NUMBERS FACTORS AND MULTIPLES 

Everywhere we turn we see numbers...on the telephone, houses, clocks, sizes , pages , money, etc. There's no escaping them! We use numbers for just about everything in our lives. Of course, one of the first things we learn is to count...one, two, buckle my shoe; three, four, shut the door, and so on. Our knowledge of numbers grows to adding money ...ummm, three dimes or 6 nickels can buy me a bag of M&M's! Communicating information using numbers is a must in this world; at work, at everyday living, as well as at play... What's the measurement of the new cabinet you just built?...How many cups of milk do I need to make 2 cakes?...How many yards do we have to run to make that touchdown? Thinking about other things in our lives in terms of numbers just seems to happen...Why does New Years Day fall on a different day of the week each year...Why 30 days in some months, 31 days in others, and let's not forget February and leap year! Using numbers to help us solve problems is the best part! This task is sometimes easier said than done. The more we learn about the properties of numbers, the better we become at using them. The more we learn, the more questions we should have and the more answers we receive, the better our understanding becomes. So, don't be afraid to ask! For instance.... Why can some numbers be divided by lots of numbers and others only by a few?

Believe it or not....
There is a quick way to determine what some of the factors of a number are without actually doing the division.
Boy is that good news....we can use all the help we can get.
Try to remember some of these facts.....
A NUMBER IS DIVISIBLE BY
2 if...it ends in a 0,2,4,6 or 8.
3 if...the sum of its digits is divisible by 3. For example, the number 135. Add its digits, 1+3+5=9. Yes, 135 is divisible by 3 because the sum of its digits, 9, is divisible by 3.
4 if...the last two digits are divisible by 4 or it ends in 00. 632...what do you think? YES!
5 if...the last digit is a 5 or 0. 25,30,35,40,45,and so on and so on...
6 if...the number is divisible by 2 and 3. For example...12,18,24 and many more! Can you think of any?
8 if... the number formed by the last two digits is divisible by 8.
9 if...the sum of the digits is divisible by 9.
10 if...the number ends in a 0. How easy is that!!!!!
Prime Factorization is a way to express a number. Any number is the product of prime numbers that have been multiplied.
WHAT AM I TALKING ABOUT????
Well, this is definately the kind of math fact that you want to see an example
of ...and fast!
Give me a number between 2 and 50
"48" Good Choice
What are the factors of 48?
(quick review)
The factor pairs are...2x24,3x16,4x12,6x8
So, the factors are 2,3,4,6,8,12,16,24
Now none of these factor pairs are the Prime Factorization because each pair includes one or more composite number as a factor.
BUT
If I keep dividing up the number 48 using prime numbers,
one of the outcomes would look like this...
48 divided by 2 = 24
24 divided by 2 = 12
12 divided by 3 = 4
4 divided by 2 = 2
If I take all the prime numbers that I used for dividing up 48, ( they are highlighted in red ), and I multiply them, the product will be 48!!!
2 x 2 x 3 x 2 = 48
or
2 x 2 x 2 x 3 = 48
or
3 x 2 x 2 x 2 x = 48
It does not matter what order you multiply these prime numbers...you will always get 48.
Most Importantly!!!!!
No matter how you choose to Prime Factor the number 48, you will ALWAYS GET THE SAME FACTORIZATION AS AN ANSWER!
Challenge
Choose a number with at least four factor pairs and find four different ways to get the prime factorization. Do you end up with the same prime factorization each time?
If you do....YOU ARE NOW A MASTER FACTOR WIZARD!
!!!CONGRATULATIONS!!!