Sponsored links: Algebra eBooks

### Related

##### gcfactor

gcfactor (7 - 4*%i);

Calculate

z1:25-5*%i;

z2:8+14*%i;

z3:1-%i;

Calculate

z1:25-5*%i;

z2:8+14*%i;

z3:1-%i;

Calculate

##### gcfactor

gcfactor(6700417);

Calculate

##### gcfactor

gcfactor(20161021);

Calculate

##### gcfactor

gcfactor( 274177);

Calculate

gcfactor(2^3);

Calculate

##### gcfactor

foo: 74*%i-11*(%i+1)^...

gcfactor(gcfactor(foo));

Calculate

z1:239+1*%i;

gcfactor(z1);

Calculate

##### gcfactor

gcfactor(20161019);

Calculate

### gcfactor

Run Example
```(%i1)? gcfactor;

-- Function: gcfactor (<n>)
Factors the Gaussian integer <n> over the Gaussian integers, i.e.,
numbers of the form `<a> + <b> `%i'' where <a> and <b> are
rational integers (i.e.,  ordinary integers).  Factors are
normalized by making <a> and <b> non-negative.

(%o1)                                true
(%i2) ```
Run Example
```gcfactor(x^2+y^2+xy-39);
2         2
(%o1)                          y  + xy + x  - 39
(%i2) ```
Run Example
```z1:25-5*%i;
(%o1)                              25 - 5 %i
(%i2)  z2:8+14*%i;
(%o2)                              14 %i + 8
(%i3) z3:1-%i;
(%o3)                               1 - %i
(%i4) d:7-4*%i;
(%o4)                              7 - 4 %i
(%i5) d:3+2*%i;
(%o5)                              2 %i + 3
(%i6) gcfactor(z1);
(%o6)              - (1 + %i) (1 + 2 %i) (2 + %i) (3 + 2 %i)
(%i7) gcfactor(z2);
2
(%o7)                 - %i (1 + %i)  (2 + %i) (3 + 2 %i)
(%i8) expand(z1/d);
25        5 %i
(%o8)                         -------- - --------
2 %i + 3   2 %i + 3
(%i9) z2/d;
14 %i + 8
(%o9)                              ---------
2 %i + 3
(%i10) ```

### Related Help

Help for Gcfactor