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Undo revision 176400 by Special:Contributions/A Noble Ox (User talk:A Noble Ox) removing vandalism
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
:<math>24 = 2 * 22 * 2 * 3 </math>
which is also written
:<math>24 = 2^3 * 3</math>.
The Prime Factorisation Theorem guarantees that every integer has one unique prime factorization, e.g. 24 =2<sup>3</sup>3<sup>1</sup>, 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
:<math>(3 + 1) * (1 + 1) = 8</math>
and they are 1, 2, 3, 4, 6, 8, 12, and 24.
[[Category:Mathematics]]
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
:<math>24 = 2 * 22 * 2 * 3 </math>
which is also written
:<math>24 = 2^3 * 3</math>.
The Prime Factorisation Theorem guarantees that every integer has one unique prime factorization, e.g. 24 =2<sup>3</sup>3<sup>1</sup>, 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
:<math>(3 + 1) * (1 + 1) = 8</math>
and they are 1, 2, 3, 4, 6, 8, 12, and 24.
[[Category:Mathematics]]