Download Factors and Multiples

Sept 1, 2011
Bellringer
Solve the following expressions.
2. 4 + 3(12 ­ 9)
1. 3 + (6 * 2)
Match the Properties with the examples.
A. 73 * 1 = 73
3. Associative
4. Commutative B. (23 + 4) + 10 = 23 +(4 +10)
C. 45 * 3 * 10 = 3 * 10 * 45
5. Identity
Aug 31­4:25 PM
Factors and
Multiples
Extraordinary made simple
TM
© 2008 SMART Technologies ULC. All rights reserved. Dec 13­1:41 PM
1
What is factoring?
Factoring a number involves breaking it down into smaller
numbers that can be multiplied together to get the original
number.
Example: 4 x 2 = 8
Factors of 8 are 4 and 2.
Sometimes, a number can be factored into different combinations.
Example: 2 x 2 x 2 = 8
Factors of 8 are also 2, 2 and 2.
Mar 19­7:45 AM
What is a prime number?
A prime number is a whole number that has exactly two factors: 1 and the
number itself.
2
Example:
1
x
The factors of 2 are 1 and 2.
This makes 2 a prime number.
2
Why is 12 not a prime number?
12
6
3
x
x 2
2
The number 12 is not a prime number because it has
more factors then 1 and itself.
Mar 19­7:45 AM
2
What is a composite number?
A composite number is a number that can be broken down into two or more
factors.
Example: factors of 16 = 1, 2, 4, 8, 16.
16 is a composite number.
What are composite numbers between 1 and 30?
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30
Mar 19­7:45 AM
b
What is prime factorization?
Prime factorization breaks down a number's factors into prime numbers.
This can be done using factor trees.
24
x
6
The prime factors of 24 are 2, 2, 2, 3.
4
HINT: Always write factors from
least to greatest.
3 x 2
2 x 2
Once you have a prime number, you stop factoring.
No matter how you break up a number, the prime factors will always end up the same.
56
7
2
2
8
2
28
14
56
The prime factors are
2, 2, 2, 7.
2
4
2
7
The prime factors are
2, 2, 2, 7.
2
Mar 19­7:45 AM
3
Use factor trees to break each
number into its prime factors.
18
41
66
Mar 19­7:45 AM
Use factor trees to break each
number into its prime factors.
16
60
100
Mar 19­7:45 AM
4
What is the greatest
common factor?
The greatest common factor of two numbers is the largest
factor shared by both. You determine the GCF by calculating
all the factors of both numbers and finding the largest one
that is a factor of both.
Example: What is the GCF of 44 and 66?
Factors of 44: 1, 2, 4, 11, 22, 44
Factors of 66: 1, 2, 3, 11, 22, 33, 66
The greatest common factor of 44 and 66 is 22.
Mar 19­7:45 AM
Find the GCF of the following
number pairs.
Factors of 18:
Factors of 24:
The greatest common factor is:
Factors of 36:
Factors of 54:
The greatest common factor is:
Mar 19­7:45 AM
5
Sept 2, 2011
Agenda: 1. Bellringer
2. Review Factors, Prime & Composite Numbers, Prime Factorization, GCF
3. Order of Operation worksheet review
4. Quiz
Bellringer: In your own words explain how to find the GCF of 10 & 25. Vocab. Review: Pass out white boards and markers to each. Students write the term they believe it right when they hear the definition.
Sep 2­11:08 AM
Find the GCF of the following
number pairs.
Factors of 8:
Factors of 80:
The greatest common factor is:
Factors of 60:
Factors of 18:
The greatest common factor is:
Mar 19­7:45 AM
6
Sept 6, 2011
Agenda: 1. Bellringer
2. Review Factors, Prime & Composite Numbers, Prime Factorization, GCF
3. Return Order of Operation worksheet
4. LCM
Bellringer: John has 72 stamps in his collection. Seaera has 63 stamps in her's. If they divided their collections into equal sized groups. How many stamps would be in each group?
D. 13
C. 21
B. 7
A. 9
Sep 2­4:45 PM
You can also find the GCF of two
numbers using prime factorization.
Example:
36
6
x
36 = 2, 2, 3, 3
54 = 2, 3, 3, 3
54
6
9
3 x 2 3 x 2
x
6
3 x 3 3 x 2
What prime factors do 36 and 54 have in
common?
36 = 2, 2, 3, 3
54 = 2, 3, 3, 3
Multiply the common prime factors together to find
the GCF.
2 x 3 x 3 = 18
The GCF of 36 and 54 is 18.
Mar 19­7:45 AM
7
Find the GCF of the following
number pairs using the prime
factorization method.
8 and 24
32 and 60
Mar 19­7:45 AM
Find the GCF of the following
number pairs using the prime
factorization method.
45 and 15
40 and 12
Mar 19­7:45 AM
8
What is the least common
multiple?
The least common multiple of two numbers is the smallest number
(not including 0 or 1) that is a multiple of both. The LCM of two
numbers is always larger then either number.
Example: What is the LCM of 3 and 4?
Multiples of 3: 3, 6, 9, 12, 15, 18...
Multiples of 4: 4, 8, 12, 16, 20...
The least common multiple of 3 and 4 is 12.
Mar 19­7:45 AM
Find the LCM of the following
number pairs.
Multiples of 2:
Multiples of 4:
The LCM of 2 and 4 is:
Multiples of 6:
Multiples of 8:
The LCM of 6 and 8 is:
Mar 19­7:45 AM
9
Find the LCM of the following
number pairs.
Multiples of 10:
Multiples of 30:
The LCM of 10 and 30 is:
Multiples of 8:
Multiples of 24:
The LCM of 8 and 24 is:
Mar 19­7:45 AM
You can also find the LCM of two
numbers using the GCF of the numbers.
Example:
Step 1: Find the GCF of the numbers 15 and 12.
Factors of 15: 1, 3, 5, 15
Factors of 12: 1, 2, 3, 4, 12
The GCF is 3.
Step 2: Multiply the original numbers together.
15 x 12 = 180
Step 3: Divide the product of the two numbers by their GCF.
108 ÷ 3 = 60
The LCM of 15 and 12 is 60.
Mar 19­7:45 AM
10
Find the LCM of the following
number pairs using the GCF method.
32 and 12
20 and 10
Mar 19­7:45 AM
Find the LCM of the following
number pairs using the GCF method.
8 and 15
15 and 30
Mar 19­7:45 AM
11
Create your own practice questions.
Mar 19­7:45 AM
12