1. An Introduction to Prime Factorization by Mrs. Gress
Growing a Factor Tree
An Introduction to Prime Factorization by Mrs. Gress

2. Objectives
This project was designed for Mrs. Gress’ fifth grade students.
There are two objectives for this lesson:
Objective #1: After using the stand-alone instructional resource, you will be able to define the term prime factorization and identify examples of prime factorization.
Objective #2: After using the stand-alone instructional resource, you will be able to solve prime factorization problems using a factor tree.

3. Related Math GLCEs
N.MR Understand the meaning of division of whole numbers with and without remainders; relate division to fractions and to repeated subtraction.
N.MR Find the prime factorization of numbers from 2 through 50, express in exponential notation, e.g., 24 = 2 3 x 31, and understand that every whole number greater than 1 is either prime or can be expressed as a product of primes.

4. Introduction
Today you will be learning how to grow a factor tree! Your job is to navigate through this presentation on your own. By doing so you will learn what the term prime factorization means and how to find the prime factorization of a number by making a factor tree.

5. A Brief Review Let's Get Started!
Before you begin growing your factor tree we must review some key terms!
What do you know about each of these terms?
Product
Factor
Prime Number
Composite Number
Let's Get Started!

6. What does “product” mean?
A product is the answer to a multiplication problem.
Product

7. What are the products?
If you said 48, 300, 36 and 160 then you’re right!
If you need more practice click the button below.
More Practice
Click here for the answers.

8. More practice with products
If you said 81, 360, 18 and 56 then you’re right!
Great Job!
If you need more help please see Mrs. Gress.
Click here for the answers.

9. What does “factor” mean?
Factors are the numbers that are multiplied together to get a product.
7 and 3 are factors of the number 21.

10. What are the factors? The factors are 6 and 8 The factors are 5 and 60
Click here for the answers.

11. What are prime numbers? An example of a prime number is 7
A prime number is a number that has exactly two factors, itself and 1.
An example of a prime number is 7
7 is a prime number because the only numbers that will divide into it evenly are 1 and 7.

12. You should memorize the first five prime numbers!
Examples of Prime #s
2, 3, 5, 7, 11, 13, 17, 19
You should memorize the first five prime numbers!
Special Note: The number 1 is not a prime number!

13. What are composite numbers?
A composite number is a number that has more than two factors.
An example of a composite number is 8
8 is a composite number because it has more than two factors. Its factors are 1, 2, 4, 8. *Hint: Remember you can make a factor rainbow!

14. Examples of Composite #s
4, 6, 8, 9, 10, 12, 14, 15
Special Note: Every whole number from 2 on is either prime or composite.

15. The Lonely Number 1
One is not a prime because it does not have exactly two different factors!
One is not a composite because it does not have more than two factors!
One is a special case! It is neither prime nor composite
Back to prime number practice

16. Practice with Primes
Click on the prime number in the list below. 9
Nice try but not quite! 9 is composite because it has three factors, 1, 3, and 9. 3
That’s right! 3 is prime because it has exactly two factors, 1 and 3. 10
Nice try but not quite! 10 is composite because it has four factors, 1, 2, 5, and 10.

17. More Practice with Primes
Click on the prime number in the list below. 1
Nice try but not quite! 1 is neither prime nor composite. Click here to read more about this special number. 15
Nice try but not quite! 15 is composite because it has four factors, 1, 3, 5, and 15. 5
That’s right! 5 is prime because it has exactly two factors, 1 and 5.

18. Practice with Composites
Click on the composite number in the list below. 2
Nice try, but not quite! 2 is a prime because it has exactly two factors, 1 and 2. 7
Nice try, but not quite! 7 is prime because it has exactly two factors, 1 and 7. 12
That’s right! 12 is composite because it has six factors, 1, 2, 3, 4, 6, and 12.

19. More Practice with Composites
Click on the composite number in the list below. 6
That’s right! 6 is a composite because it has four factors, 1, 2, 3, and 6. 23
Nice try, but not quite! 23 is prime because it has exactly two factors, 1 and 23. 3
Nice try, but not quite! 3 is prime because it has exactly two factors, 1 and 3.

20. What is Prime Factorization?
Look at the equations on the right. What pattern do you notice? Write down what you notice in your math notebook.
Click here for a hint?
Look at the factors? What kind of numbers are they?

21. What does “factor” mean?
Factors are the numbers that are multiplied together to get a product.
7 and 3 are factors of the number 21.
Back to Prime Factorization

22. A Definition
Hopefully you noticed that each of the factors in the equations are prime numbers.
Prime Factorization is a way to write a composite number as a product of prime factors.

23. Growing a Factor Tree
To find the prime factorization of a number you can grow a factor tree!
Let’s get started.

24. Getting Started
You might notice that 180 has a ZERO in its ONES PLACE which means it is a multiple of 10. So…
10 x  = 180
10 x 18 = 180
Can you think of one factor pair for 180?
This should be two numbers that multiply together to give you 180.
180
Let’s grow a tree of the factors of 180. 10 18
Click here to continue
Click here to continue

25. What’s Next?
We “grow” this “tree” downwards since that is how we write in English (and we can’t be sure how big it will be - we could run out of paper if we grew it upwards).
180
Now you have to find factor pairs for 10 and 18. 10 18

26. Keep Growing Down 180 10 18 2 5 6 3 First find two factors of 10.
Click here to continue
Next find factors for 18.
Click here to continue 10 18 2 5 6 3
2 x 5 = 10
6 x 3 = 18

27. Are We Done Yet???
Since 2, 3, and 5 are prime numbers they do not grow “new branches” they just grow down alone.
Click here to continue
180
Since 6 is NOT a prime number - it is a COMPOSITE NUMBER - it still has factors. Since it is an EVEN NUMBER we see that:
6 = 2 x 3 10 18 2 5 6 3 2 5 2 3 3

28. Are We Done Yet???
180
Now that the bottom row of our tree is made up of all prime factors we have found the prime factorization.
There is only one more step! 10 18 2 5 6 3 2 5 2 3 3

29. The Final Step
All we have left to do is write the equation. Make sure you write the numbers in order from least to greatest!
180 10 18 2 5 6 3 2 5 2 3 3

30. So….
The prime factorization of the composite number 180 is…

31. You will need to draw your factor tree in your math notebook.
Now You’re Ready…
to grow your own factor tree!
You will need to draw your factor tree in your math notebook.

32. Find the prime factorization of 63
Remember, first you find two factors of 63. 9 7
These two factors multiply together to give you the product 63.
Now you try! First check to see if either number is prime. If a number is prime bring it straight down. (Remember 1 is not a prime number so it should not be part of your prime factorization!)

33. Find the prime factorization of 63
Your factor tree should now look like this! 9 7 7
Next, look at the other number and find two factors that multiply together to give you that number. Extend your tree!

34. Find the prime factorization of 63
Your factor tree should now look like this! 9 7 3 3 7
Now, if all of your numbers are prime then you are done. If not, keep extending your tree.

35. Find the prime factorization of 63
Since 3, 3, and 7 are all prime numbers you are done!
All you need to do is write it as an equation. 9 7 3 3 7

36. It’s Quiz Time Let’s see what you know!
You will need a blank piece of paper. Please make sure you put your name, number, and the date on the top.
You will need to draw a factor tree for each of the problems. This will be turned in to Mrs. Gress when you are done.

37. Question #1
What is the prime factorization of 27? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

38. Since 3 is a prime number the prime factorization of 27 is 3 x 3 x 3.
That’s Correct! 27 9 3 3 3 3
Since 3 is a prime number the prime factorization of 27 is 3 x 3 x 3.

39. Not Quite! Try again!
9 is a composite number so 3 x 9 can’t be the prime factorization of 27 because all the numbers are not prime.

40. Not Quite! Try again!
9 is a composite number and 1 is neither prime nor composite, so 3 x 9 x 1 can’t be the prime factorization of 27 because all the numbers are not prime.

41. Question #2
What is the prime factorization of 40? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

42. That’s Correct! 40 8 5 4 2 5 2 2 2 5
Since 2 and 5 are both prime numbers the prime factorization of 40 is 2 x 2 x 2 x 5.

43. Not Quite! Try again!
2 x 2 x 5 equals 20, not 40 so it can’t be the prime factorization of 40.

44. Not Quite! Try again!
4 is a composite number, so 4 x 2 x 5 can’t be the prime factorization of 40 because all the numbers are not prime.

45. Question #3
What is the prime factorization of 100? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

46. That’s Correct!
100 10 10 2 5 2 5
Since 2 and 5 are both prime numbers the prime factorization of 100 is 2 x 2 x 5 x 5.

47. Not Quite! Try again!
4 is a composite number, so 4 x 5 x 5 can’t be the prime factorization of 100 because all the numbers are not prime.

48. Not Quite! Try again!
4 is a composite number, so 4 x 2 x 5 can’t be the prime factorization of 40 because all the numbers must be prime.

49. Question #4
What is the prime factorization of 36? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

50. That’s Correct! 36 6 6 2 3 2 3
Since 2 and 3 are both prime numbers the prime factorization of 36 is 2 x 2 x 3 x 3.

51. Not Quite! Try again!
6 is a composite number, so 6 x 2 x 3 can’t be the prime factorization of 36 because all the numbers are not prime.

52. Not Quite! Try again!
6 is a composite number, so 6 x 6 can’t be the prime factorization of 36 because all the numbers are not prime.

53. Question #5
What is the prime factorization of 14? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

54. That’s Correct! 14 2 7
Since 2 and 7 are both prime numbers the prime factorization of 14 is 2 x 7.

55. Not Quite! Try again!
1 is neither prime nor composite, so 1 x 1 x 2 x 7 can’t be the prime factorization of 14 because all the numbers are not prime.

56. Not Quite! Try again!
2 x 3 x 4 equals 24, not 12 so it can’t be the prime factorization of 12.

57. Question #6
What is the prime factorization of 110? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

58. That’s Correct!
110 10 11 2 5 11
Since 2, 5, and 11 are all prime numbers the prime factorization of 110 is 2 x 5 x 11.

59. Not Quite! Try again!
2 x 2 x 5 x 11 equals 220, not 110 so it can’t be the prime factorization of 110.

60. Not Quite! Try again!
10 is a composite number, so 10 x 11 can’t be the prime factorization of 110 because all the numbers are not prime.

61. Question #7
What is the prime factorization of 63? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

62. That’s Correct! 63 9 7 3 3 7
Since 3 and 7 are both prime numbers the prime factorization of 63 is 3 x 3 x 7.

63. Not Quite! Try again!
9 is a composite number, so 9 x 7 can’t be the prime factorization of 63 because all the numbers are not prime.

64. 7 x 7 equals 49, not 63 so it can’t be the prime factorization of 63.
Not Quite! Try again!
7 x 7 equals 49, not 63 so it can’t be the prime factorization of 63.

65. Question #8
What is the prime factorization of 250? (Remember to draw your factor tree on your paper before you try to answer the question!) A. B. C.

66. That’s Correct!
250 10 25 2 5 5 5
Since 2 and 5 are both prime numbers the prime factorization of 250 is 2 x 5 x 5 x 5.

67. Not Quite! Try again!
10 is a composite number, so 10 x 5 x 5 can’t be the prime factorization of 150 because all the numbers are not prime.

68. Not Quite! Try again!
2 x 2 x 5 x 5 equals 100, not 250 so it can’t be the prime factorization of 100.

69. Congratulations! You have done a great job growing your factor trees!
Please turn in the eight factor trees from the quiz to Mrs. Gress.
and
Don’t forget to keep practicing!