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Properties Review 
Math Properties Multiples
Question:What is a Multiple?
Answer:
When you skip count, you are saying multiples of a number.
Multiples of any number are the products of that number and any whole number.
Example:
Find 8 multiples of 5 starting with 5.
Strategy: Skip Count by 5s Starting with 5. (Number Line)
5, 10, 15, 20, 25, 30, 35, 40
Example:
Find 6 multiples of the number 6.
Strategy: Multiply
1 6 x 1 = 6
2 6 x 2 = 12
3 6 x 3 = 18
4 6 x 4 = 24
5 6 x 5 = 30
6 6 x 6 = 36
6, 12, 18, 24, 20, 30, 36 are all multiples of 6.
Math Alert:
You can multiply any number by zero. When you do so the product is zero. Usually when we list multiples of a number, we do no list zero.
Least Common Multiples (LCM)
Question:What is a Least Common Multiple?
Answer:
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both.
Example:
Find the LCM of 6 and 9.
Strategy: Find the first few multiples of both numbers.
Step 1: Find the first six multiples of 6.
6, 12, 18, 24, 30, 36
Step 2: Find the first six multiples of 9.
9, 18, 27, 36, 35, 54
Step 3: Find the smallest number that is a multiple of both 6 and 9.
Common multiples of 6 and 9 are 18 and 36.
18 is the smallest multiple that is common to both 6 and 9.
The LCM of 6 and 9 is 18.
Factors & Common Factors
Question:What is a Factor?
Answer:
The factors of a number are the counting numbers that evenly divide that number. Counting numbers are 1, 2, 3, 4, and so on
Question:
What are Common Factors?
Answer:
A group of two or more whole numbers may have some factors that are the same. These factors are called common factors.
Example:
Find the Factors of 6.
Strategy: Think about the counting numbers you can multiply to get a product of 6.
1 x 6 = 6 1 and 6 are factors of 6.
2 x 3 = 6 2 and 3 are factors of 6.
Example:
Find the Common Factors of 16 and 24.
Strategy: Venn Diagram
Find The Common Factors of 16 and 24.
16 = 16 x 1
16 = 2 x 8
16 = 4 x 4
24 = 1 x 24
24 = 2 x 12
24 = 3 x 8
24 = 4 x 6
The Common Factors of 16 and 24 are 1, 2, 4, and 8
Greatest Common Factors (GCF)
What is a greatest common factor (GCF)?The greatest common factor (GCF) of two numbers is the greatest number that is a factor of both numbers.
Example:
Find the GCF of 27 and 45.
Strategy: Find the factors of each number first.
Step 1: Find the factors of 27.
The factors of 27 are 1, 3, 9, and 27
Step 2: Find the factors of 45.
The factors of 45 are 1, 3, 5, 9, 15, and 45.
Step 3: What is the greatest factor that both numbers have in common?
Common factors of 27 and 45 are 1, 3, 5, 9, 15, 45.
The GCF of 27 and 45 is 9.
Example:
Find the GCF of 6 and 12.
Strategy: Venn Diagram
Find The Factors Of 6:
6 = 1 x 6
6 = 2 x 3
Find The Factors of 12:
12 = 1 x 12
12 = 2 x 6
12 = 3 x 4
Common Factors:
1, 2, 3, 6, 12
GCF:
12
Prime & Composite Numbers
What is a Prime Number?A prime number is a counting number that has exactly two different factors, one and itself.
Example:
2 is a prime number because it is divisible by only 1 and 2.
What is a Composite Number?
A composite number is a counting number that has more than two different factors.
Example:
8 is a composite number because it has more than two different factors: 1, 2, 4, 8.
Math Alert:
One is Not Prime!
1 is a lonely number because it is nether prime or composite. It’s not a prime because it does not have exactly two different factors. It’s not composite because it does not have more than two factors.
