Download Factors and Multiples

Factors and Multiples
Factors and multiples are both to do with multiplication:
Factors are what you can multiply to get a number
Multiples are what you get after multiplying a number by an
integer.
Factors
"Factors" are the numbers you can multiply together to get
another number: 2 and 3 are factors of 6
A number can have many factors.
Example:
3 and 4 are factors of 12, because 3×4=12
Also 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 ALL the factors of 12 are 1, 2, 3, 4, 6 and 12
Greatest Common Factor (GCF)
The highest number that divides exactly into two or more numbers.
It is the "greatest" thing for simplifying fractions!
Greatest Common Factor of 12 and 16
1. Find all the Factors of each number,
2. Circle the Common factors,
3. Choose the Greatest of those
What is a "Common Factor"?
Let us say you have worked out the factors of two numbers:
÷6
Example: Factors of 12 and 30
12
2
Factors of 12 are 1, 2, 3, 4, 6 and 12
=
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
30
5
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
÷6
It is a common factor when it is a factor of two or more numbers. (It is then
"common to" those numbers.)
The largest or greatest of these common factors is 6. So 6 is the Greatest Common Factor
Why is this Useful?
One of the most useful things is when we want to simplify a fraction:
Example: How could we simplify 12/30?
Earlier we found that the Common Factors of 12 and 30 were 1, 2, 3 and 6, and so the Greatest
Common Factor is 6.
So the largest number we can divide both 12 and 30 evenly by is 6, like this:
The Greatest Common Factor of 12 and 30 is 6.
And so 12/30 can be simplified to 2/5
Finding the GCF can also be used in problems such as:
A room that is 20 m by 12 m is to be tiled with square tiles. If the tiles must fit perfectly without
cutting and be a whole number of metres on each side, what is the largest tile size that could
be used?
Finding the Greatest Common Factor
1. Factor Rainbow



find all factors of both numbers,
then select the ones that are
common to both, and,
then choose the greatest.
Example: The GCF of 18 and 24
Two Numbers
Factors
18 and 24
18: 1,2,3,6,9,18
24: 1,2,3,4,6,12, 24
Common Factors
1,2,3,6
Greatest
Example Simplified
Common Factor
Fraction
6
2. Factor Tree: You can find the prime factors by using a Factor Tree:
The first step you take is to use factor trees to find the
prime factors of both 16 and 24.
18/
24
= 3/4
After you've determined that 16's prime factors are 2 • 2 • 2 • 2
and that 24's prime factors are 2 • 2 • 2 • 3, you'll want to write
those two rows of factors one above the other, then circle the
factors that both 16 and 24 have in common:
\At this point you're going to ignore the prime factors
that 16 and 24 don't have in common. Take the
common prime factors (in this case three sets of 2) and
multiply the 2s one time for each circle:
Least Common Multiple (LCM)
The smallest (non-zero) number that is a multiple of two or more numbers.
What is a "Multiple"? A multiple is the result of multiplying a number by an integer (not a
fraction).
Example:
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, etc ...
Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, etc.
What is the "Least Common Multiple"?
When you list the multiples of two (or more) numbers, and find the same value in both lists, then that
is a common multiple of those
numbers. The LCM is simply the
smallest of the common multiples.
As you can see on this number line,
the first time the multiples match up
is 15. Answer: 15
You can also find the least common multiple of 3 (or more) numbers.
Example: Find the least common multiple for 4, 6, and 8
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
Multiples of 8 are: 8, 16, 24, 32, 40, ....
So, 24 is the least common multiple
Finding the LCM can help with fractions to determine the least common denominator. It can also help
with questions like this:
Kyle bought some $12 shirts. Jack bought some $15 shirts. They both spent the same amount
of money, which was less than $200. How much money could they have spent?