Now that you have learned how to find the factors of a number in skill #3, you can move on to finding prime and composite numbers!
So, what is a prime number? It is a number that only has two factors: ONE and ITSELF.
For example, the number 7 can only be divided by 1 and 7. It has no other factors. That makes 7 a PRIME number!
What other prime numbers can you think of? (1, 3, 5, 7...) notice a pattern? But be careful! Not all odd numbers are prime. The number 9, for example, also has 1, 3, and 9 as factors which makes it a composite number.
A composite number is any integer (number) that more than the two factors of one and itself. For example, the number 24 has the factors 1, 2, 3, 4, 6, 8, 12 and 24! That makes it a COMPOSITE number. What other composite numbers can you think of?
Here are two hints about composite numbers:
What about larger numbers? How can you tell if they are prime or composite numbers?
Hint #1: All even numbers are composite numbers.
Hint #2: All numbers ending in 5 or 0 are composite (because they will have at least a factor of 5).
For the rest of the numbers, we can find the factors like we did with Skill #3 (by creating a number line) or with a new strategy called "Factor Trees".
Take a look at this sample factor tree for the number 48. You can start by dividing the number by one of its' factors (in this case, they chose the number 2). Most mathematicians start with the number two for any even number. Since the number 2 is a prime number, I can stop trying to branch out that number and instead focus on 24. See how they divided 24 into the branches of 2 and 12?
To finish a factor tree, continue breaking down each composite number until you are left with only prime numbers. You can write an expression for what is called the PRIME FACTORIZATION of the original number by multiplying all of the prime numbers that you found (in this case 2 x 2 x 2 x 2 x 3 = 48).