### The Maxima on-line user's manual

Algebra Calculator

#### Ifactors

Function: ifactors (<n>) For a positive integer <n> returns the factorization of <n>. If `n=p1^e1..pk^nk` is the decomposition of <n> into prime factors, ifactors returns `[[p1, e1], ... , [pk, ek]]`.

Factorization methods used are trial divisions by primes up to 9973, Pollards rho method and elliptic curve method.

```          (%i1) ifactors(51575319651600);
(%o1)     [[2, 4], [3, 2], [5, 2], [1583, 1], [9050207, 1]]
(%i2) apply("*", map(lambda([u], u[1]^u[2]), %));
(%o2)                        51575319651600```

```(%o1)                                true
(%i2) ```

### Related Examples

##### ifactors-random

joukko:[30, 42, 70];

luku: joukko[random(3)];

ifactors(luku);

Calculate

##### ifactors

ifactors(909808);

Calculate

##### ifactors-matrix

m:matrix([1,1,-1],[1,...

eq1:x+y-z=0;

eq2:x+5*y+z=0;

Calculate

##### ifactors

ifactors (1000000000);

2^9;

5^9;

Calculate

##### ifactors

ifactors(168166253272...

(1816625327230064)*(1...

Calculate

primep(5434652);

p:325231;

ifactors(p);

Calculate

ifactors(20);

Calculate

##### ifactors-totient

ifactors(1919191238);

1919191238*(1-1/2)*(1...

totient(1919191238);

Calculate

##### ifactors-primep

primep(15318947608);

p:131;

ifactors(p);

Calculate

##### ifactors

ifactors(34035);

(3-1)*(5-1)*(2269-1);

Calculate