Difference between revisions of "Factor"
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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 | + | :<math>24 = 2 * 2 * 2 * 3 </math> |
which is also written | which is also written | ||
| − | :24 = 2^3 * 3. | + | :<math>24 = 2^3 * 3</math>. |
| − | Every integer has | + | Every integer has 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 exponents of prime factors 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 exponents of prime factors 2 and 3 are 3 and 1, respectively. The number of divisors of 24 is therefore | ||
| − | :(3 + 1) * (1 + 1) = 8 | + | :<math>(3 + 1) * (1 + 1) = 8</math> |
and they are 1, 2, 3, 4, 6, 8, 12, and 24. | and they are 1, 2, 3, 4, 6, 8, 12, and 24. | ||
Revision as of 21:03, March 27, 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 factorization of 24 is
which is also written
.
Every integer has 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 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.
