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By K. Lee Lerner, Brenda Wilmoth Lerner

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Gordon Miller Botanist Corvallis, Oregon Kelli Miller Science Writer NewScience Atlanta, Georgia Christine Miner Minderovic Nuclear Medicine Technologist Franklin Medical Consulters Ann Arbor, Michigan David Mintzer Professor Emeritus Department of Mechanical Engineering Northwestern University Evanston, Illinois Christine Molinari Science Editor University of Chicago Press Chicago, Illinois Frank Mooney Professor Emeritus Fingerlake Community College Canandaigua, New York Partick Moore Department of English University of Arkansas at Little Rock Little Rock, Arkansas Robbin Moran Department of Systematic Botany Institute of Biological Sciences University of Aarhus Risskou, Denmark J.

For instance, 12 can be factored into the product 6 ϫ 2, or 3 ϫ 4. The expression (x2 - 4) can be factored into the product (x + 2)(x - 2). Factor is also the name given to the parts. We say that 2 and 6 are factors of 12, and (x-2) is a factor of (x2 - 4). Thus we refer to the factors of a product and the product of factors. The fundamental theorem of arithmetic states that every positive integer can be expressed as the product of prime factors in essentially a single way. A prime number is a number whose only factors are itself and 1 (the first few prime numbers are 1, 2, 3, 5, 7, 11, 13).

A prime number is a number whose only factors are itself and 1 (the first few prime numbers are 1, 2, 3, 5, 7, 11, 13). Integers that are not prime are called composite. The number 99 is composite because it can be factored into the product 9 ϫ 11. It can be factored further by noting that 9 is the product 3 ϫ 3. Thus, 99 can be factored into the product 3 ϫ 3 ϫ 11, all of which are prime. By saying “in essentially one way,” it is meant that although the factors of 99 could be arranged into 3 ϫ 11 ϫ 3 or 11 ϫ 3 ϫ 3, there is no factoring of 99 that includes any primes other than 3 used twice and 11.

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