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#### Search: #### 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^u), %));
(%o2)                        51575319651600```

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

### Related Examples

##### ifactors

ifactors(111111111111...

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##### ifactors

ifactors(152411252);

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ifactors(991);

mod(563,13);

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##### ifactors-primep

primep(32523112);

p:325231;

ifactors(p);

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primep(153146);

p:131;

ifactors(p);

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##### ifactors-primep

primep(3542436256123);

p:325231;

ifactors(p);

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##### ifactors

ifactors(123456789012...

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ifactors(9);

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##### ifactors-primep

primep(542436256);

p:325231;

ifactors(p);

Calculate

##### ifactors-mod

ifactors(181);

ifactors(991);

mod(563,13);

Calculate 