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The Maxima on-line user's manual

Algebra Calculator

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Ifactors 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]].

ifactors(563);
mod(73,3);

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) 

Ifactors Example

Related Examples

ifactors-mod

ifactors(429);

mod(563,11);

Calculate

ifactors-primep

primep(542436256);

p:325231;

ifactors(p);

Calculate

ifactors-primep

next_primep(45641);

p:45641;

ifactors(p-1);

Calculate

ifactors-primep

primep(325231);

p:325231;

ifactors(325231);

Calculate

ifactors-next_prime

p1:next_prime(1111112...

p2:next_prime(4534576...

p:p1*p2;

Calculate

ifactors-mod

ifactors(181);

ifactors(991);

mod(991,181);

Calculate

ifactors-random

var1: random(2500);

var2: ifactors(var1);

var2[1];

Calculate

ifactors

ifactors(123456789012...

Calculate

ifactors

ifactors(10010);

ifactors(360);

Calculate

ifactors-phi

phi(n) := ifactors(n) ;

phi(10);

Calculate