# Question #490ed

Apr 12, 2017

Prime numbers have exactly $2$ factors.

#### Explanation:

Count the number of factors that a number has.

A PRIME number has exactly TWO factors - 1 and itself.

The first prime numbers are:

$2 \text{ "3" "5" "7" "11" "13" "17" "19" "23" "29" "31" } 37. \ldots .$

1 is not a prime number becasue it only has ONE factor - $1$

Numbers which have THREE or more factors are COMPOSITE.

Here is a list of the factors of the numbers up to 12.

$1 : \rightarrow 1$
$2 : \rightarrow \textcolor{red}{1 , \text{ } 2}$
$3 : \rightarrow \textcolor{red}{1 , \text{ } 3}$
$4 : \rightarrow 1 , \text{ "2," } 4$
$5 : \rightarrow \textcolor{red}{1 , \text{ } 5}$
$6 : \rightarrow 1 , \text{ "2," "3," } 6$
$7 : \rightarrow \textcolor{red}{1 , \text{ } 7}$
$8 : \rightarrow 1 , \text{ "2," "4," } 8$
$9 : \rightarrow 1 , \text{ "3," } 9$
$10 : \rightarrow 1 , \text{ "2," "5," } 10$
$11 : \rightarrow \textcolor{red}{1 , \text{ } 11}$
$12 : \rightarrow 1 , \text{ "2," "3," "4," "6," } 12$

The prime numbers are shown in red:
They all have exactly $2$ factors.