All composite numbers can be factored out into its prime roots. This is called prime factorization. There are several ways of doing this, as shown below.
The Factor Tree
This is the most common method of prime factorization, done by repetitively extracting prime-numbered factors from the given number until all the roots are prime.
For example, the number 162 can be factored as shown below:
Continuous Division by Prime Numbers
This method is quite similar to the factor tree in such a way that the principle used in factorization is the same. The only difference is that you divide the given number until you reach 1. Here is the way it is illustrated:
Fermat's Prime Factorization Method
Perhaps this is the most technical of all the methods given in this discussion. Yet it is the most algebraically based. Discovered by Pierre Fermat, this process is composed of three major steps:
Here is an example:
x = 667
The square root of 667 is 25.8263, which is 26 when rounded off.
The square of 26 is 676. Thus, m2 - x = 676 - 667 = 9.
In the form m2 - s2 = x, the equation would be:
262 - 32 = 667
(26-3) (26+3) = 667
(23) (29) = 667
Thus you would get two values that is almost impossible to get using the previous two methods (unless you are a mathematician): 23 and 29.
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