To divide is to perform the operation of division, i.e., to see how many times a divisor 
goes into another number 
. 
divided by 
is written 
or 
. The result need not be an
integer, but if it is, some additional terminology is
used. 
is read "
divides 
" and means that 
is a divisor of 
. In this case, 
is said to be divisible by 
. Clearly, 
and 
.
By convention, 
for every 
except 0 (Hardy and Wright 1979, p. 1). The "divisibility" relation
satisfies
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where the symbol 
means implies.
is read "
does not divide 
" and means that 
is not a divisor of 
. 
means 
divides 
exactly. If 
and 
are relatively prime, the notation 
or sometimes 
is used.
