audio read-through Prime Numbers

The numbers $\,2, 3, 4,\, \ldots\,$ can be expressed as products in a very natural way! Just keep ‘breaking them down’ into smaller and smaller factors until you can't get the ‘pieces’ any smaller.

For example:






No matter how the number is ‘broken down’, you'll always get to the same place, except for possibly different orderings of the factors.

In the example above, you always get: $$360 = 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 5$$ Three factors of $\,2\,,$ two factors of $\,3\,,$ and one factor of $\,5\,.$

These smallest ‘pieces’ (like $\,2\,,$ $\,3\,$ and $\,5\,$ above) are, in a very real way, basic ‘building blocks’ for numbers being represented as products. They're very, very, very important! So, you shouldn't be surprised that these ‘multiplicative building blocks’ are given a special name:

DEFINITION prime numbers
A counting number greater than $\,1\,$ is called prime if the only numbers that go into it evenly are itself and $\,1\,.$

Notes on the Definition



Concept Practice