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In [[integer]] arithmetic, a '''factor''' is an integer that evenly divides another integer. For example, 3 is a factor of 24 because 24 divied 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 expreesion of an integer as a product of its prime factors is called a '''prime factorization'''. The prime factorization of 24 is
*24 = 2 * 2 * 2 * 3
which is also written
*24 = 2^3 * 3.
Every integer has a one unique prime factorization, though it may have multiple non-prime factorizations (e.g. 24 = 2 * 12, 24 = 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 exponts of 2 and 3 are 3 and 1, respectively. The number of divisors of 24 is therefore
(3 + 1) * (1 + 1) = 8
and they are 1, 2, 3, 4, 6, 8, 12, and 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 expreesion of an integer as a product of its prime factors is called a '''prime factorization'''. The prime factorization of 24 is
*24 = 2 * 2 * 2 * 3
which is also written
*24 = 2^3 * 3.
Every integer has a one unique prime factorization, though it may have multiple non-prime factorizations (e.g. 24 = 2 * 12, 24 = 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 exponts of 2 and 3 are 3 and 1, respectively. The number of divisors of 24 is therefore
(3 + 1) * (1 + 1) = 8
and they are 1, 2, 3, 4, 6, 8, 12, and 24.