FactorInteger

FactorInteger(n)

returns the factorization of n as a list of factors and exponents.

FactorInteger(n, GaussianIntegers->True)

for gaussian integers you can set the option GaussianIntegers->True

See

• Wikipedia - Integer factorization
• Wikipedia - Prime number

Examples

>> FactorInteger(990)
{{2,1},{3,2},{5,1},{11,1}}

>> FactorInteger(341550071728321)
{{10670053,1},{32010157,1}}

>> factors = FactorInteger(2010)
{{2, 1}, {3, 1}, {5, 1}, {67, 1}}

To get back the original number:

>> Times @@ Power @@@ factors
2010

FactorInteger factors rational numbers using negative exponents:

>> FactorInteger(2010 / 2011)
{{2, 1}, {3, 1}, {5, 1}, {67, 1}, {2011, -1}}

Gaussian integers:

>> FactorInteger(10+30*I, GaussianIntegers->True)
{{-1,1},{1+I,3},{1+I*2,1},{2+I,2}}

>> FactorInteger(11+14*I, GaussianIntegers->True)
{{11+I*14,1}}

Implementation status

• ✅ - full supported

Github

• Implementation of FactorInteger