In Mathematical Terms, What Does “factor” Mean?

VikramRaghuvanshi/E+/Getty Images

A factor is a number or expression that divides another number or expression evenly without a remainder. For instance, two, four, five and 10 are factors of 20 because 20 can be divided by all those smaller numbers an exact number of times. Prime numbers are positive integers greater than one that have exactly two factors. A composite number has more than two factors.

Another way to define a factor is to multiply two or more numbers together to produce a larger number. All of those smaller numbers are factors of the product. A factor is also a divisor of a product, meaning the larger number is divided by the smaller an exact number of times.

Prime numbers have two factors, the prime number itself and one. Two is a prime number because two and one are the only numbers that multiply together to make two. Seven is a prime number because one and seven are the only numbers that produce seven as a multiple.

Factoring large whole numbers has a practical use in computer cryptography. Internet transactions are encrypted on the user and merchant end by large prime-number keys that complete the transactions. Without factoring of prime numbers, encryption codes over the Internet would not exist.