What is Prime Factorization and how is a Factor Tree used?
Here is a Merriam-Webster Dictionary definition "any of the numbers or symbols in
mathematics that when multiplied together form a product". Stated more simply, a
large number can be broken down in to a group of smaller Prime Numbers; when the smaller numbers are multiplied
together, you get the original larger number. Example: the number 12 can be factored
into 2 x 2 x 3 = 12. Note 12 is not a prime number
but its factors are all prime. This example demonstrates Prime Factorization.
Prime Factorization can be organized in a Factor Tree
for ease of viewing. There may be more than one valid factor tree
for the same number, but the prime factors at the end are always the same. Before
going further, here is recommended reading: Exponents. The factor tree for 108
is shown below:
Prime Factorization Using A Factor Tree
| 108
|
| 2
|
54
|
| 2
|
27
|
| 3
|
9
|
| 3
|
3
|
As you can see the prime factors of 108
follow: 108 = 3 x 3 x 3 x 2 x 2 = 33 x 22 .
| 1 |
x |
108 |
= |
108 |
| 2 |
x |
54 |
= |
108 |
| 2 |
x |
27 |
= |
54 |
| 3 |
x |
9 |
= |
27 |
| 3 |
x |
3 |
= |
9 |