Download Prime Factors

Prime Factors
Prime Numbers
A Prime Number can be divided evenly only by 1 or itself.
And it must be a whole number greater than 1.
Example:
7 can only be divided evenly by 1 or 7, so it is a prime number.
But 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number (it is a
composite number).
Factors
Any number that goes into 12 is called a factor of 12. That number, with
some other number, will multiply to give 12.
e.g
4 is a factor of 12. It partners with 3. And 4 x 3 = 12.
List of All Factors
For any number, we can make a list of all the factors.
e.g. for 12: 1, 2, 3, 4, 6, 12 is a list of all the factors:
Prime Factors
The prime factors of a number are simply all the numbers in the factor
list that are also PRIME.
e.g. for 12: 1,2,3,4,6, and 12 are all the factors.
Out of these, only 2 ane 3 are PRIMES.
So the prime factors of 12 are 2 and 3.
Factor Trees
What is a factor tree?
A factor tree for 36 looks like the image below:
A factor tree starts with a number at the top. If a number is
“composite”, then it will be split into 2 on the line below. Notice the 2
branches off 36. In this particular tree, the 36 is being split into 9 and 4.
This can be done because 9 x 4 = 36. Note if you multiply everything in
the 2nd line together, 9 x 4, you get 36 (the original number).
On the second line, notice that 9 and 4 are also composite.
So we split both 9 and 4 into 2 parts, where the 2 parts multiply together
to give that number. So we use 3 x 3 for 9, and 2 x 2 for 4.
Notice if we multiply everything on the 3rd row together,
we get 3 x 3 x 2 x 2 = 9 x 4 = 36.
Notice that all 4 numbers on the 3rd row are prime. Once we get a prime
number, you can’t split it into 2 factors (unless you use 1 an itself). This is
pointless. We never use ‘1’s in a factor tree.
So the aim of a factor tree is to keep splitting composite numbers into 2
until we have nothing but primes left.
The reason we want to do this is we can find out WHAT PRIMES make up
that original number.
In this case, 36 is made up of 3 x 3 x 2 x 2. So its prime factors are 3
and 2.
Some Examples
Note, 90 can be split into 9 and 10.
On the next line, 9 is split into 3 and 3. 10 is split into 5 and 2.
On the third line, everything is prime, so we stop.
Note, 42 can be split into 6 x 7.
On the next line, the 7 is already prime, so note it is not split. I simply
bring it down. But the 6 can be split into 2 and 3.
IN THIS EXAMPLE, primes that are discovered earlier than the end are
BROUGHT DOWN each time. Doing a Factor Tree this way means that
each line can be read as a way of representing 42.
Note 6 x 7 = 42 (2nd line). And 2 x 3 x 7 = 42 (3rd line).
Some factor trees do NOT BOTHER to bring down primes.
Check the factor tree below out:
Notice that the tree just “stops” when a prime is reached. The reason
this can be annoying is, because if you want to find all the primes at the
end, you have to go and circles all the “ends” of the tree.
So the prime factors of 48 are 2, 2, 2, 3, and 2. In other words, 2 and 3
are the only prime factors.
I don’t like this way as it fails to make the connection between each line
and the original number. If we redo this tree, bringing the primes down
until the last level, we get:
Now I see that
8 x 6 – 28.
And 4 x 2 x 3 x 2 = 8 x 6 = 48.
And finally 2 x 2 x 2 x 3 x 2 = 4 x 2 x 3 x 2 = 8 x 6 = 48.
There is More Than One Way To Do Factor
Trees
Check out the 2 factor trees below for the number 36.
Both are correct. The reason you have multiple factor trees is because
there is more than one way to split some numbers (multiple factor pairs).
You should never worry about whether or not your factor tree looks
exactly like the answer. The only important part is the bottom line.
And even then, look carefully. The order of the primes doesn’t matter.
Simply which ones are there (order of multiplication is not important).
The 2 trees above might look like they have different answers, but BOTH
contain two 2s and two 3s at the end… so they are the same.