Factors & Multiples - Brown
GCF - The Greatest Common Factor
...The greatest common factor of two or more numbers is the greatest of their common factors. The abbreviation GCF is often used for greatest common factor.
What are the factor pairs of 24?
1 and 24, 2 and 12, 3 and 8, 4 and 6
List the factor pairs for the number 48.
1 and 48, 2 and 24, 3 and 16, 4 and 12, 6 and 8
What are 72's factors?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
What is the LCM of 20 and 25?
100
Example of a composite number and why it's a composite number
12 is composite number because 1, 2, 3, 4, 6, and 12 all go into 12
What are the first 6 multiples of 12?
12, 24, 36, 48, 60, 72
What are the first three multiples of 13?
13, 26, 39
What are the first 5 common multiples of 35 and 7?
35, 70, 105, 140, 175,
Example of a factor
6 is a factor of 30
Examples of relatively prime numbers
8 and 5, 3 and 4, 6 and 7 are examples of relatively prime numbers, because each pair only shares 1 as a common factor.
Factor Pair
A factor pair for a number is two factors whose product equals that number.
Multiple
A multiple of a whole number is the product of that number and another whole number.
Common Factor
A number that is a factor of 2 or more numbers
What is a "Common multiple"
A number that is a multiple of two or more numbers Example: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, etc Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, etc Common Multiples of 3 and 4: 12, 24, 36
Composite number
A whole number greater than 1 with more then two factors
Example of Prime Factorization
An example of the prime factorization of 48 is 2•2•2•2•3 (2 to the 4th power times 3)
Question: Is 1,001 a prime number?
Answer: No because 1,001 has more than 2 factors: 1, 7, 11, 13, 1001.
Find the GCF of 21 and 49
Answer: The GCF of 21 and 49 is 7
Is 101 a prime number? Why or why not?
Answer: Yes since 101 has no factors besides itself and 1.
Key word: prime number
Definition: A number that can only be divisible by itself and 1.
Key word Prime Number
Definition: A number that only has 2 factors: 1 and itself
Example of Prime Numbers
List examples: 3, 7, 11, 13, 17, 19, 23, 29
Question: Is 37 a composite number?
No, it is a prime number.
Find the GCF of 18 and 24
The GCF of 18 and 24 is 6
Example of GCF
The GCF of 24 and 30 is 6
Example of LCM
The LCM (Least Common Multiple) of 12 and 18 is 36
An example of an LCM
The LCM of 10 and 15 is 30
What is the LCM of 20 and 50?
The LCM of 20 and 50 is 100
Example of LCM
The LCM of 5 and 10 is 10
What is the LCM of 40 and 70?
The answer is 280
Example of a Factor Pair
The factor pairs of 28 are: (1, 28), (2, 14), (4, 7)
Example of a multiple
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, etc.
What is the prime factorization of 120?
The prime factorization of 120 is 2•2•2•3•5. It can also be written as 2 to the 3rd power * 3 * 5.
Prime Factorization
When you list a composite number as a product of only prime numbers
Question: Is 39 a composite number?
Yes, it is a composite number because it has more than 2 factors: 1, 3, 13, 39
Can two even numbers (higher than 2) be relatively prime? Yes or no?
no, because they would always have '2' as another common factor.
Is 7 and 10 relatively prime? yes or no
yes, because their only common factor is 1.
