Difference between revisions of "Factor"
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Factors are sometimes called '''divisors''' to distinguish them from '''prime factors'''. A prime factor is a divisor that is a [[prime number]]. 2 and 3 are prime factors of 24. 6 is not a prime factor because it is a [[composite number]]. | Factors are sometimes called '''divisors''' to distinguish them from '''prime factors'''. A prime factor is a divisor that is a [[prime number]]. 2 and 3 are prime factors of 24. 6 is not a prime factor because it is a [[composite number]]. | ||
| − | The expression of an integer as a product of its prime factors is called a '''prime factorization'''. The prime | + | The expression of an integer as a product of its prime factors is called a '''prime factorization'''. The prime factorisation of 24 is |
| − | :<math>24 = 2 * | + | :<math>24 = 2 * 22 * 2 * 3 </math> |
which is also written | which is also written | ||
Revision as of 09:45, May 25, 2007
A factor is an integer that evenly divides another integer. For example, 3 is a factor of 24 because 24 divided by 3 does not leave a remainder. 5 is not a factor of 24.
Factors are sometimes called divisors to distinguish them from prime factors. A prime factor is a divisor that is a prime number. 2 and 3 are prime factors of 24. 6 is not a prime factor because it is a composite number.
The expression of an integer as a product of its prime factors is called a prime factorization. The prime factorisation of 24 is
which is also written
.
The Prime Factorisation Theorem guarantees that every integer has one unique prime factorization, e.g. 24 =2331, though it may have multiple non-prime factorizations (e.g. 24 = 2 * 12, 6 * 4, 3 * 8).
The number of divisors of an integer may be determined from its prime factorization when expressed in exponent form, by incrementing each exponent by 1 and multiplying the results. In the example above, the exponents of prime factors 2 and 3 are 3 and 1, respectively. The number of divisors of 24 is therefore
and they are 1, 2, 3, 4, 6, 8, 12, and 24.
