An integer is any positive or negative whole number. Zero is also an integer, but fractions, decimals and imaginary numbers are not integers.
Integers can be arranged consecutively on a number line. Negative integers are to the left of zero and positive integers are to the right. The relative position of two integers on a number line allows you to compare their values. Integers can be added, subtracted, multiplied and divided. They are either even, in that they can be divided by two without leaving a remainder, or odd numbers.
Any integer can be expressed as the product of prime numbers. Remember that a prime number has only two factors, one and itself. For example, 42 is a positive whole number, an integer. 42 = 7 x 3 x 2. Seven, three and two are all prime numbers.
Mathematicians arrange into sets groups of numbers that share attributes. The set of all integers has a name, Z. Another set of integers include just the positive integers. This set is called N.
The word integer comes from the Latin. It means whole, complete, perfect or virtuous. We also get the word integrity from the same Latin root, so it is easy to remember that an integer must always be a whole number.