In mathematics, a factor of a number is a number that divides the given number evenly or exactly, leaving no remainder
. Factors are only considered for positive integers, and they cannot be fractions or decimals
. To check if a number x is a factor of a certain number n, simply divide n by x. If the remainder is 0, then x is a factor of n. Otherwise, x is not a factor of n
. Some important facts about factors include:
- If a number has more than two factors (but a finite number of factors), it is called a composite number
- Factors are never decimals or fractions; they are only integers
- All even numbers have 2 as a common factor
- 5 is a factor of all numbers that end in 0 and 5
- All numbers ending in a 0 have 2, 5, and 10 as factors
Factoring is a crucial step in solving many algebraic problems and is of great importance in public-key cryptography
. The prime factors of a number or an algebraic expression are those factors that are prime, meaning they have only two factors (i.e., themselves and 1)
. By the fundamental theorem of arithmetic, except for the order in which the prime factors are written, every whole number larger than 1 can be uniquely expressed as the product of its prime factors
. For example, 60 can be written as the product 2·2·3·5
