## Testing if a Number is Prime

A positive whole number
$n$
is prime if it is divisible by just two numbers - 1 and itself.
1 is not a prime number.
We can test if a number
$n$
is prime by dividing by all the whole numbers up to and including

.
We need not go so far. In fact we need only divide by the prime numbers up to
$\sqrt{n}$
.
Example: is 77 prime?$\sqrt{77} =8.7....$
so we nee only divide by prime numbers up to and including 8.
. These are 2, 3, 5, 7
$\frac{77}{2}=38.5$

$\frac{77}{3}=32.66666....$

$\frac{77}{5}=15.4$

$\frac{77}{7}=11$

Hence
$77=11 \times 7$
is nor prime.