Embedded Files
Videos
Videos
The Ladder Method
The Ladder Method
Factoring
Factoring
Prime Factorization
Prime Factorization
GCF
GCF
Finding LCM
Factors
Factors
Numbers we can multiply together to get another number.
Example: 2 and 3 are factors of 6, because 2 × 3 = 6
A number can have MANY factors!
Example: What are the factors of 12?
• 3 × 4 = 12, so 3 and 4 are factors of 12
• 2 × 6 = 12, so 2 and 6 are also factors of 12
• and 1 × 12 = 12, so 1 and 12 are factors of 12 as well
So 1, 2, 3, 4, 6 and 12 are all factors of 12
Multiples
Multiples
We get a multiple of a number when we multiply it by another number. Such as multiplying by 1, 2, 3, 4, 5, etc, but not zero. Just like the multiplication table.
Here are some examples:
The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...
The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...
Greatest Common Factor
Greatest Common Factor
What is a "Common Factor" ?
What is a "Common Factor" ?
Say we have worked out the factors of two numbers:
Example: Factors of 12 and 30
Example: Factors of 12 and 30
Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
Then the common factors are those that are found in both lists:
Notice that 1, 2, 3 and 6 appear in both lists?
So, the common factors of 12 and 30 are: 1, 2, 3 and 6
It is a common factor when it is a factor of two (or more) numbers.
Here is another example with three numbers:
Example: The common factors of 15, 30 and 105
Example: The common factors of 15, 30 and 105
Factors of 15 are 1, 3, 5, and 15
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
Factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105
The factors that are common to all three numbers are 1, 3, 5 and 15
In other words, the common factors of 15, 30 and 105 are 1, 3, 5 and 15
What is the "Greatest Common Factor" ?
What is the "Greatest Common Factor" ?
It is simply the largest of the common factors.
In our previous example, the largest of the common factors is 15, so the Greatest Common Factor of 15, 30 and 105 is 15
The "Greatest Common Factor" is the largest of the common factors (of two or more numbers)
Why is this Useful?
Why is this Useful?
One of the most useful things is when we want to simplify a fraction.
Least Common Multiple
Least Common Multiple
What is a "Common Multiple" ?
What is a "Common Multiple" ?
When we list the multiples of (for example) 4 and 5, the common multiples are those that are found in both lists:
The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...
The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...
Notice that 20 and 40 appear in both lists?
So, the common multiples of 4 and 5 are: 20, 40, (and 60, 80, etc ..., too)
What is the "Least Common Multiple" ?
What is the "Least Common Multiple" ?
It is simply the smallest of the common multiples.
In our previous example, the smallest of the common multiples is 20 ...
... so the Least Common Multiple of 4 and 5 is 20.
Finding the Least Common Multiple
Finding the Least Common Multiple
List the multiples of the numbers until we get our first match.
Information in this section corresponds to: 8.1 Factors and Multiples, and 8.5 Greatest Common Factor and Least Common Multiple: Beckmann, Sybilla. Mathematics for Elementary Teachers with Activities (p. 337-339, 356-359). Pearson Education.
Information in this section corresponds to: 8.1 Factors and Multiples, and 8.5 Greatest Common Factor and Least Common Multiple: Beckmann, Sybilla. Mathematics for Elementary Teachers with Activities (p. 337-339, 356-359). Pearson Education.
Page updated
Report abuse