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Prime Factorization
2-1
http://www.brainpop.com/math/numbersandoperations/
factoring/
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http://www.brainpop.com/math/numbersandoperations/factoring/quiz/
Answers:
1. C2. D3. B4. A5. A6. D7. C8. B9. C10. A
Divisible
When a number can be divided by a second number and have a
remainder of zero.
8 / 4 = 2 18 / 9 = 2
81 / 9 = 9
Divisibility Rules
The Rule for 2
If a number is even, then it is divisible by two.– An even number is any number that
ends in a 2, 4, 6, 8, or 0
52100
98
7693
Div
isib
ility
Ru
les
The Rule for 3
Add up all the digits. If the sum of all digits is divisible by
3, then the whole number is divisible by 3!
6321 = 6 + 3 + 2 + 1 =123 goes into 12 evenly, so 6321 is divisible by
3
63 981 21 762
28
The Rule for 4
The last two numbers are either 00 or they are divisible by 4.– An even number is any number that
ends in a 2, 4, 6, 8, or 0
804
724600
916
217
The Rule for 5
The number ends in a 5 or a zero.
55 100
90 75
93
The Rule for 6
If divisible by 2 and 3.
55 100
90 75
93
Add up all the digits. If the sum of all digits is divisible by
9, then the whole number is divisible by 9!
6327 = 6 + 3 + 2 + 7 =189 goes into 18 evenly, so 6327 is divisible by
9
The Rule for 9
81
1125414 882312
The Rule for 10
The number ends in a zero
5840
1020
6430
70
9003
Factor
The numbers that are multiplied to get a product
15 = 3 x 53 and 5 are factors of 15
2 x 9 = 182 & 9 are factors of
18
3 x 2 =63 & 2 are
factors of 6
Prime Number
is a counting number that only has two factors, itself and one.
One is not a prime
7 is a prime5 is a
prime
Composite Number
Numbers which have more than two factors (such as six, whose factors are 1, 2, 3 and 6)
One is not a composite
8 is a composite55 is a
composite
A Rhyme to Help Us Remember
Prime numberPrime numberWhat do you see?I see no other factorsExcept for one and me.
Composite numberComposite numberWhat do you see?I see at least three factorsIncluding one and me.
1 2 3 4 5 6 7 8 9 10
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All of the orange numbers on this chart are prime. Write them down. Refer to them so you don’t waste time trying to factor them.
Prime Factorization
When a composite number is written as a product of all of its prime factors
Using the Factor Tree
78 / \ / \ 2 x 39 / / \ / / \ 2 x 3 x 13
Let’s Try a Factor Tree!
84 / \
2 x 42 / / \ 2 x 2 x 21 / / / \ 2 x 2 3 x 7
Factor Trees do not look the same for the same number,
but the final answer is the same.
72 / \
8 x 9 / \ / \
2 x 4 x 3 x 3 / \ 2 x 2 x 2 x 3 x 3
72 / \
2 x 36 / / \ 2 x 2 x 18 / / / \ 2 x 2 x 2 x 9 / / / / \ 2 x 2 x 2 x 3 x 3
Greatest Common Factor
The largest common factor of 2 or more numbers
Use prime factorization or ladder to find GCF
GCF of 36 and 24Is 12
GCF of 72 and 84Is 12
Prime Factorization is helpful for finding
greatest common factors. 72
/ \ 8 x 9 / \ / \
2 x 4 x 3 x 3 / \ 2 x 2 x 2 x 3 x 3
Take the common prime factors of each number and multiply to find the greatest common factor.
84
/ \ 2 x 42
/ / \ 2 x 2 x 21 / / / \ 2 x 2 3 x 7
2 x 2 x 3 = 12
Use the Ladder for LCM, GCF and Simplifying Fractions
WRITE the two numbers on one line.
DRAW THE L SHAPE DIVIDE out common
prime numbers starting with the smallest
722 84362 42183 21
6 7
LCM makes an L: LCM = 2 2 3 6 7 = 504
GCF = 2 2 3 = 12
8472
=76
GCF is down the left side:
Simplified fraction is on the bottom
Use the Ladder for LCM, GCF and Simplifying Fractions
WRITE the two numbers on one line.
DRAW THE L SHAPE DIVIDE out common
prime numbers starting with the smallest
242 36122 18
63 92 3
LCM makes an L: LCM = 2 2 3 2 3 = 72
GCF = 2 2 3 = 12
3624
=32
GCF is down the left side:
Simplified fraction is on the bottom
Use the Ladder for LCM, GCF and Simplifying Fractions
WRITE the two numbers on one line.
DRAW THE L SHAPE DIVIDE out common
prime numbers starting with the smallest
111 1311 13
LCM makes an L: LCM = 11 13 = 163
GCF = 1GCF is down the left side:
Simplified fraction is on the bottom
HOMEWORK
PG 558 – 38 evens
24 – 30 use ladder method to find GCF
32 – 38 use prime factorization to find GCF (trees)
Resources
Brain Pop – Prime Factors Brain Pop - Prime Numbers Brain Pop - Exponents
Interactive Practice for Factor Trees
1. Virtual Manipulatives2. Interactive Practice 13. Interactive Practice from MathPlayground.
com
The Birthday Cake Method
a.k.a. The Box Method
An alternative to factor trees
A video from YouTube
Challenge Problem Use what you know about multiplying
whole numbers by variables and exponents to make a factor tree for the following monomial
45x3
45
x3
x x x59
33
A Random Thought about Prime Numbers
Brought to you from YouTube.com
Use the Ladder for LCM, GCF and Simplifying Fractions
WRITE the two numbers on one line.
DRAW THE L SHAPE DIVIDE out common
prime numbers starting with the smallest
242 36122 18
63 92 3
LCM makes an L: LCM = 2 2 3 2 3 = 72
GCF = 2 2 3 = 12
3624
=32
GCF is down the left side:
Simplified fraction is on the bottom
