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Factoring
Factors
Factors - Whole numbers that are multiplied
to find a product are called factors of that
product. A number is divisible by its factors.
2·3=6
6 ÷ 3 = 2 6 is divisible
by 3 and 2
Factors Product
6÷2=3
Factoring Numbers
Factoring a number means finding its factors.
Basically you have to figure out what you
could divide a number by without anything
leftover. (no remainder). There are 2 ways to
do this. (well, there are actually more… but for
our purposes we are only going to look at 2)
Method 1: Listing
List the factors in pairs.
18:
1 · 18
2·9
3·6
1 is a factor. 2 is a factor. 3 is a factor. 4 is not a
factor. 5 is not a factor. 6 has already been
listed. So STOP here.
You can draw a diagram to illustrate the factor
pairs.
18: 1 2 3 6 9 18
Method 2: Prime Factorization
The prime factorization of a number is written
as the product of its prime numbers. To find
those prime numbers you create a factor tree.
Like monkeys swinging on the lowest branches
of the trees, prime numbers swing off the
lowest branches of factor trees.
* See I told you to stick with me on the monkey
thing
Let’s say you want to factor 30.
Draw two little branches coming down from
the number. Ask yourself, “ What are two
numbers that when multiplied together give
you 30?”
How about 15 and 2? Then look at both of
these numbers and ask the same question.
For 15 we can split it into 3 and 5. But for 2 it
is already prime. Yes, like a monkey. We then
circle the “monkeys” to keep track of them.
And what about 3 and 5? They are both
monkeys as well, so they also get circled.
30
15
5
2
3
*No matter how you start a factor tree, you’ll
always end up with the same prime #’s.
• Each of the circled numbers is prime, so we’re
done. The prime factorization of 30 is 2 · 3 · 5.