https://www.alpertron.com.ar › GAUSSIAN.HTM

This Web application factors Gaussian integers as a product of Gaussian primes. The Gaussian integers are complex numbers of the form a + b i, where both a and b are integer numbers and i is the square root of -1.

https://www.thinkcalculator.com › numbers › factorize-gaussian-integer.php

Gaussian integer factorizations. A Gaussian integer is either the zero, one of the four units (± 1, ± i). For the rational prime 5, Gaussian integer factorizations of 5 = (−i) (2 + i) (1 + 2i).

https://www.wolframcloud.com › objects › demonstrations › FactoringGaussianIntegers-source.nb

Factoring Gaussian Integers. 10i+18 (7-2i)(-i) 3. (i+1) Every nonzero Gauss. an. nteger. a+b. , where. and. b. are ord. nary. ntegers and. = -1. , can be expressed un. que. y as the product of a un. t and powers of spec. a. Gauss. an pr. mes. Un. ts are 1, , -1, - Spec. a. Gauss. an pr. mes are. 1+. and pr. mes. z.

https://stackoverflow.com › questions › 2269810

To find the Gaussian primes with norm p, just use Euclid's algorithm (slightly modified to work with Gaussian integers) to compute the GCD of (p, k+i). That gives one trial divisor. If it evenly divides the Gaussian integer we're trying to factor (remainder = 0), we're done. Otherwise, its conjugate is the desired factor.

https://www.had2know.org › academics › gaussian-integer-factorization.html

You can use the calculator at left to factor any Gaussian integer where a and b are not equal to zero. To factor integers and pure imaginary numbers over the Gaussian primes, use the other calculator. Gaussian Prime Factorization of a Gaussian Integer. First, divide out the GCD of a and b to form a reduced Gaussian integer.

https://en.wikipedia.org › wiki › Table_of_Gaussian_Integer_Factorizations

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.

https://www.foxcalculators.com › math › 1426.html

Factorization: A Gaussian integer is either the zero, one of the four units (± 1, ± i). For the rational prime 5, Gaussian integer factorizations of 5 = (−i) (2 + i) (1 + 2i).

https://www.alpertron.com.ar › CALTORS.HTM

Gaussian Integer Factorization applet: Finds the factors of complex numbers of the form a+bi where a and b are integers. It also includes a complete calculator with operators and functions using gaussian integers.

https://mathworld.wolfram.com › GaussianInteger.html

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q (sqrt (-1)) and form a ring often denoted Z [i], or sometimes k (i) (Hardy and Wright 1979, p. 179).