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The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 104: 2 3 ·13 ...
Factorization: 2 3 × 13: Divisors: 1, 2, 4, 8, 13, 26, 52, 104: ... 104 (one hundred [and] four) is the natural number following 103 and preceding 105. In mathematics
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of ...
The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, = =). This theorem is one of the main reasons why 1 is not considered a prime number : if 1 were prime, then factorization into primes would not be unique; for example, 2 = 2 ⋅ 1 = 2 ⋅ 1 ⋅ 1 ...
Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...
The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime. The factorizations take the form of an optional unit multiplied by integer powers of Gaussian primes. Note that there are rational primes which are not Gaussian primes.
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This followed the factorization of HP49(110) on 8 September 2012 [2] and of HP49(104) on 11 January 2011, and prior calculations extending for the larger part of a decade that made extensive use of computational resources.