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Growing Prime Factorization TreesMrs. Shaw 6th Grade Math
Warm Up
Practice your multiplication Math facts up to 12 x 12 in one of the following ways:
By yourself using the My Math App on the iPad or on your iPhone
By yourself using an Internet browser and going to http://www.ixl.com/math/grade-3/multiplication-facts-to-12
QUIETLY with a partner using flashcards.
Research Prime and Composite Numbers
Using a textbook or the Internet, answer the following questions in your Math journal.
What is a prime number?What is a composite
number?
What is a Prime Number?
A whole number greater than 1 that can only be divided evenly by 1 and itself.
A whole number greater than 1 that only has two whole number factors, 1 and itself.
Prime Numbers
Is 0 or 1 a prime number?NO! Prime numbers must be GREATER than 1.
0 1
How about 1.4, 2.5, or 3/2?
NO! Prime numbers must be WHOLE numbers.
No decimals or fractions!
Examples
2 3 5 7
What is a Composite Number?
A whole number greater than 1 that can be evenly divided by at least one whole number that is not 1 or itself.
A whole number greater than 1 that has at least three whole number factors including 1 and itself.
Composite numbers are the whole numbers greater than 1 that are not prime numbers.
Composite Numbers
Is 0 or 1 a composite number?NO! Composite numbers must be GREATER than 1.
0 1 How about 1.4, 2.5, or 3/2?
NO! Composite numbers must be WHOLE numbers, too.
No decimals or fractions!
Examples4 has three factors: 1, 2 and 4 6 has four factors: 1, 2, 3, and 6
Identify the Prime Numbers less than 100
On your worksheet, mark out all the numbers that are not prime numbers.
Mark out 0 and 1 because 0 and 1 are not prime numbers.
Remember!!! 0 and 1 are not composite either!
First, Mark Out 0 and 1
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Identify the Prime Numbers less than 100
Notice that 2 is a prime number because it only has two factors: 1 and itself, 2.
All even numbers greater than 2 are not prime because they have at least three factors, 1, itself, AND 2.
Mark out all the even numbers greater than 2.
Next, Mark Out the Even Numbers Greater
Than 20 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Identify the Prime Numbers less than 100
Like 2, 3 is a prime number because it only has two factors: 1 and itself, 3.
All the other multiples of 3 have at least three factors: 1, itself, AND 3. So, all other multiples of 3 are not prime.
Mark out all the other multiples of 3.
Next, Mark Out the Multiples of 3 Greater Than 3
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Identify the Prime Numbers less than 100
5 and 7 are prime numbers, right? Why?
Because they each only have two factors:1 and itself.
Like you did for multiples of 2 and 3, mark out the other multiples of 5 and 7.
Next, Mark Out the Multiples of 5 Greater Than 5
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Next, Mark Out the Multiples of 7 Greater Than 7
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Because all the multiples of of the other prime numbers, 11, 13, 17, ...
are already marked out, WE’RE DONE!
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Did you notice that all Composite Numbers are multiples of Prime
Numbers?You can write any composite number as the product of prime numbers by factoring and factoring, again and again, until you can factor no more.
Let’s look at an example: 36
36 = 2 X 18
36 = 2 X 2 X 9
36 = 2 X 2 X 3 X 3
This is called PRIME FACTORIZATION.
Notice What It Looks Like If I Write It This Way
36
2 X 18
2 X 2 X 9
2 X 2 X 3 X 3
Writing it like this makes it look like a tree!
So we call these
PRIME FACTORIZATION TREES!
When I Say “Prime Factorization” You Say “Tree”
Prime Factorization
TREE
Prime Factorization
TREE
Prime Factorization
TREE
Whenever you are asked to find the prime factors of a number, just remember you need to “grow a
factor tree”.
Growing Healthy Looking Trees
When factoring a composite number, always start with the lowest prime number factor so that your trees grow neatly down and towards the right, with the like factors in a neat diagonal line. 24 24 /\ /\ 2 12 2 12 /\ /\ 2 6 6 2 /\ /\ 2 3 3 2
Let’s Try Some Together
35 /\ 5 7
What is the lowest prime number that evenly divides into 35?
Does 2? No, 35 is not an even number.
Does 3?No, 35 is not evenly divisible by 3.
Does 5?Yes, 5 times 7 is 35. And 7 is prime so we are done!
Let’s Try Another Together
What is the lowest prime number that evenly divides into 42?
Does 2? Yes, 42 is an even number.
What is the lowest prime number that evenly divides into 21?
Not 2, does 3? Yes, 3 times 7 is 21. And 7 is prime so we are done!
42 /\ 2 21 /\ 3 7
56 /\ 2 28 /\ 2 14 /\ 2 7
It’s Your Turn To Guide Me
72 /\ 2 36 /\ 2 18 /\ 2 9 /\ 3 3
Try some on your own
99 /\ 3 33 /\ 3 11
64 /\ 2 32 /\ 2 16 /\ 2 8 /\ 2 4 /\ 2 2
Homework
You can use your calculator to help you identify the prime factors, but be sure to write down all the branches of the trees.
Homework will be graded tomorrow after Warm Up.
Website to explore prime numbers (Go ahead, try it!):http://www.math.com/students/calculators/source/prime-number.htm
KhanAademy Websites to help you review:http://www.khanacademy.org/math/arithmetic/factors-multiples/prime_numbers/v/prime-numbers
http://www.khanacademy.org/math/arithmetic/factors-multiples/prime_factorization/v/prime-factorization
