Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors.

1. What is the difference between prime
and composite numbers?
List the first six prime numbers.

2. Prime #: only divisible by two numbers.
Composite #: are divisible by three or
more numbers.
First six prime numbers:
2, 3, 5, 7, 11, 13

3. Learning Target:
Students will learn how to write whole
numbers as the product of prime
factors called prime factorization while
reviewing the meaning of prime and
composite numbers.

4. Factors are the different groups that a
number can be split into evenly.
Ex. 27 factors are: 1,3,9,27
1 group of 27
3 groups of 9
9 groups of 3
27 groups of 1

5. To find factors - I think about finding
the pot of gold at the end of a rainbow.
36: 1, 2, 3, 4, 6 , 9, 12, 18, 36

6. Keep in mind your Divisibility Rules:
2: # is even (ends in 0,2,4,6,8)
3: if the sum of the digits
is divisible by 3
5: if it ends in a 0 or 5
6: if it is even and divisible by 3
9: if the sum of the digits is
divisible by 9
10: if it ends in a 0

7. List all the factors of the number.
8
18

8. Answers:
8: 1, 2, 4, 8
18: 1, 2, 3, 6, 9, 18

9. How could you rewrite 42 as the
product of only prime numbers?

10. 42 = 2 x 3 x 7
Prime Factorization: is when you write
a number as the product of prime
numbers.

11. There are two diagrams you can use to
write the factorization of a number.
1. Factor Tree
2. Ladder

12. Factor Tree
Prime Factorization is 2x2x2x2x3 = 24x3
48
2 24
2 2 12
2 2 2 6
2 2 2 2 3

13. Ladder: 2, 3, 5, 7, 11, 13
2 48
2 24
2 12
2 6
3 3
1
Prime factorization is 2x2x2x2x3 = 24x3

14. Ladder:
Ask each time is your number you have
divisible by 2. Try 2 until it doesn’t
work any more then try 3. Try 3 until it
doesn’t work any more and so on. You
are finished when you reach the
number 1.

15. Find the prime factorization of the
number.
90
200

16. Answers:
90: 2 x 3 x 3 x 5 = 2 x 32 x 5
200: 2 x 2 x 2 x 5 x 5 = 23 x 5

17. Can you write whole numbers as the
product of prime factors?
Can you list factors of a number?