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:

$360$$=$$36$$\cdot$$10$
 $=$$6$$\cdot$$6$$\cdot$$2$$\cdot$$5$
 $=$$2$$\cdot$$3$$\cdot$$2$$\cdot$$3$$\cdot$$2$$\cdot$$5$
OR
$360$$=$$4$$\cdot$$90$
 $=$$2$$\cdot$$2$$\cdot$$9$$\cdot$$10$
 $=$$2$$\cdot$$2$$\cdot$$3$$\cdot$$3$$\cdot$$2$$\cdot$$5$
OR
$360$$=$$6$$\cdot$$60$
 $=$$2$$\cdot$$3$$\cdot$$6$$\cdot$$10$
 $=$$2$$\cdot$$3$$\cdot$$2$$\cdot$$3$$\cdot$$2$$\cdot$$5$

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:

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
The Prime Factorization Theorem

 
 


    
(an even number, please; MAX is 30)
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6 7 8 9 10 11 12
AVAILABLE MASTERED IN PROGRESS

(MAX is 12; there are 12 different problem types.)