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An '''integer''' is any whole number, positive, negative, or 0.  More precisely, the set of all integers consists of all natural numbers {1, 2, 3, 4, ...}, their negatives {-1, -2, -3, -4, ...} and 0.  A formal definition is that it is the only [[integral domain]] whose positive elements are well ordered and in which order is preserved by addition.

An '''integer''' is any whole number, positive, negative, or 0.  More precisely, the set of all integers consists of all natural numbers {1, 2, 3, 4, ...}, their negatives {-1, -2, -3, -4, ...} and 0.  A formal definition is that it is the only [[integral domain]] whose positive elements are well ordered and in which order is preserved by addition.

An integer may be even (divisible by two) or odd (not divisible by two), positive (more than [[zero]]) or negative (less than zero), whole (undivided) or fractional (divided into smaller parts), and various other classifications, such as [[prime]] (only divisible by itself and one).

An integer may be [[even number|even]] (divisible by two) or [[odd number|odd]] (not divisible by two), [[positive number|positive]] (more than [[zero]]) or [[negative number|negative]] (less than zero), [[whole number|whole]] (undivided) or fractional (divided into smaller parts), and various other classifications, such as [[prime]] (only divisible by itself and one).

Every integer larger than 1 has a unique [[prime factorizarion]].

Every integer larger than 1 has a unique [[prime factorizarion]].