Elementary arithmetic, with brief notices of its history... by Robert Potts.

ON PRIME AND COMPOSITE NUMBERS.
MEASURES AND MULTIPLES.
ART. 1. There are certain relations and properties of numbers of
extensive use in almost all arithmetical operations, which are also
necessary in the arithmetic of fractions and decimals.
In the series of natural numbers, 1, 2, 3, 4, 5, 6, &c., a distinction
may be observed of odd and even numbers. An odd number is one
which cannot be divided into two equal whole numbers, as 1, 3, 5, 7,
9, &c. An even number is one which can be divided into two equal
whole numbers, as 2, 4, 6, 8, &c.
There is another, a more important division of the natural numbers
into two classes, one class consisting of numbers, each of which is
divisible only by 1 and a number equal to itself, as 2, 3, 5, 7, 11,
&c.; and the other class consisting of numbers which admit of other
divisors, as 4, 6, 8, 9, 10, &c. The numbers in the former class are
called prime number s; and those in the latter class, composite cumbers.
DEF. A prime number is one which can be exactly divided only
by unity and a number equal to itself.
DEF. A composite number is a number which is composed of the
product of two or more prime numbers; or, a composite number may
be defined to be a number which admits of other divisors than unity
and a number equal to itself.
DEF.. A multiple of a number is any number of times that number;
as 12 is a multiple of 3 and of 4, for 12 is 4 times 3, and 3 times 4.
Both 3 and 4 are called szubmultiples of 12.
DEF. One number is said to be a measure of another, when the
former is contained in the latter a certain number of times exactly; as
3 is a measure of 12, for 3 is contained 4 times exactly in 12.
The terms mnultiple and mneasure are only other.names for dividend
and divisor in cases where there is no remainder after division, and
are thus related: since 3 is a divisor of 12, it follows that 12 is
a multiple of 3.
DEF. A con2mmon measiure or common divisor of two or more numbers,
is a number which will divide exactly each of them; and the greatest
number which will exactly divide each of them is called their greatest
common measure; thus 3 is a common measure of 12 and 18, but 6
is their greatest common measure.
When two or more numbers have no common measure except 1,
they are said to be prime to each other, as 2 and 3, 4 and 5, 6 and
35; and all prime numbers are prime to one another; but composite
numbers may be, or may not be, prime to one another.