Multiples
(from mathsisfun.com)
What is a "Multiple" ?
The multiples of a number are what you get when you multiply it by other
numbers (such as if you multiply it by 1,2,3,4,5, etc). Just like the multiplication
table.
Here are some examples:
Again, it doesn’t make sense to say “36 is a multiple”… you need to say “36 is a
multiple of 2” or “36 is a multiple of 6” or “36 is a multiple of 12” etc.
How do you make a list of multiples of a certain number?
There are 2 ways:
Method 1: Find all the answers to the times tables for that number
e.g. MULTIPLES OF 3
3 x 1, 3 x 2, 3 x 3, 3 x 4, 3 x 5, 3 x 6, 3 x 7, 3 x 8, ... etc. etc.
Note: they go on forever. We get 3, 6, 9, 12, 15, 18, 21, 24, …
Method 2: Start at the number (the first multiple of any number is itself) and
then just keep “adding” the number itself to the last multiple.
e.g. MULTIPLES OF 3
Start at 3.
3 + 3 = 6.
6 + 3 = 9.
9 + 3 = 12.
12 + 3 = 15.
15 + 3 = 18.
… etc. etc.
One is NOT a multiple of any whole number except 1?
Students often start a list of multiples with ‘1’ (because the first factor is always
1). However, this is WRONG. 1 is NOT an answer to the 3 times tables. So it
shouldn’t be in the list of MULTIPLES OF 3.
THE FIRST MULTIPLE of any number is ITSELF.
Factors and Multiples : Not Getting Confused
MULTIPLES you get by MULTIPLYING. MULTIPLES must be EQUAL or
BIGGER than the number you are working with.
FACTORS you get by FITTING IN WITHOUT REMAINDER. FACTORS must be
LESS THAN or EQUAL to the number you are working with.
Example: Make a list of BOTH the factors of 12 and the first 5 multiples of
12.
Solution:
Factors fit in. Numbers that fit into 12 are 1,2,3,4,6,12.
Multiples come from multiplying by 12. 12 x 1 = 12. 12 x 2 = 24. 12 x 3
= 36. 12 x 4 = 48. 12 x 4 = 50. So the first 5 multiples are 12, 24, 36,
48, 60.
NOTE: You can’t choose how many factors a number has… you just have
to try and find them all. But with multiples, there are infinitely many, so
you always have to say HOW MANY you want when making a list.
Language Associated with Factors and Multiples
If 12 is a multiple of 2, then 2 must be a multiple of 24. That’s because factors
make multiples, and thus multiples must be made up of factors.
In a “What’s my age” question, if the age is 60 we could say 2 things which mean
exactly the same:
6 is a factor of my age…. OR my age is a multiple of 6.
NOTE each clue is exactly the same, just written differently.
**Extra: Computer Programs Can Find Multiples For You
If you can create the following Scratch program (code provided), note how it will
give you a list of all the multiples that the user asks for ANY NUMBER they ask.
Here is the clear button to do after each try: