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Line 1: − + − *24 = 2 * 2 * 2 * 3 + − *24 = 2^3 * 3.+ Line 15:
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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 divided by 3 does not leave a remainder. 5 is not a factor of 24.
In [[integer]] arithmetic, 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]].
Factors are sometimes called '''divisors''' to distinguish them from '''prime factors'''. A prime factor is a divisor that is a [[Prime Number|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 factorization of 24 is
The expression 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
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).
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
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
:(3 + 1) * (1 + 1) = 8
and they are 1, 2, 3, 4, 6, 8, 12, and 24.
and they are 1, 2, 3, 4, 6, 8, 12, and 24.