Prime Numbers

A special case of algebra factoring

is when we don't find many factors for a number but just two: 1 and the number itself:

For example:

2 = 1 x 2 = 1 + 1

3= 1 x 3 = 1 + 1 + 1

5= 1 x 5 = 1 + 1 + 1 + 1 + 1

7= 1 x 7 = 1 + 1 + 1 + 1 + 1 + 1 + 1

Well, these special numbers are called prime numbers.

All other numbers which do have more factors are called composite numbers instead.

So, they are like little gems, building up a numerical mathematical skeleton.

To find out which ones they are, we must proceed with a (simple) procedure (an algorithm) which keep asking us the ordered sequence of divisibility rules of an "in crescendo" (upwards) series of prime numbers.... 2,3,5,7,11,13,17,23, etc...

Yes divisibility by 2,3,5,7,11,13,17,23, etc...

This is called factorization.

It's easier to illustrate this concept with an example.

But beforehand, you should but refresh the divisibility rules. Moreover, you can also make use of this software which I tried out and found quite well made... despite the usual American (commercial) idea of forcing fun in learning... (and the voices are ugly, the interactivity can also be improved, but the content is ok). Provided you really use it without getting distracted....

Prime factorization for the number 36

36 is divisible by 2 ---------------------> 36 : 2 = 18
18 is divisible by 2 ---------------------> 18 : 2 = 9
9 is divisible by 3 -----------------------> 9 : 3 = 3
3 is divisible by 3 only (prime) --------> 3 : 3 = 1

so,

We can see that we used the factor "2" two times (36:2 and 18:2) and the factor "3" 2 times (9:3 and 3:3). In fact 36 = 2x2x3x3. We can also write this (we'll come later to this strange way of mathematical writing convention, called "exponentials") as:

What we did is the prime factorization of the number 36

Alternatively you can check my factorization calculator webpage (to be used as a way to control a result, NOT as a a shortcut from studying!).

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