# Maple -- computing all possible divisors of an integer

Discussion in 'Undergraduate Math' started by Jenny C, Oct 24, 2006.

1. ### Jenny CGuest

Hey,
When using maple to find all divisors of a large integer, how do we compute
these divisors from the knowledge of its prime factorisation. I'm sure the
first step would be to use the ifactor command but then what's next...
Any suggestions....?
Thanks

Jenny C, Oct 24, 2006

2. ### Arturo MagidinGuest

If you know the prime factorizatio of n,

n = p_1^{a_1} * ... * p_r^{a_r}

where p_i is a prime, p_i different from p_j, and a_i are positive
integers, then every divisor must be of the form

d = p_1^{b_1}* ... * p_r^{b_r}, with b_i integers satisfying
0<= b_i <= a_r

If you know the primes and the exponents for n, this can easily be
done with some recursion.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

Arturo Magidin, Oct 24, 2006

3. ### PubkeybreakerGuest

Take the prime factors 1 at a time, 2 at a time, 3 at a time, .......

Pubkeybreaker, Oct 24, 2006
4. ### kilian heckrodtGuest

if you know the prime factorisation already you just modify/iterate the
exponents for each factor.
if you are factorization is: p_1^k_1*....p_n^k_n then you create all
products p_1^i_1*....p_n^i_n with 0<=i_j<=k_j for j=1..n
programmatically you could do that with loop(s) or a recursion, however
in maple yopu could use the "seq" command as well.

kilian heckrodt, Oct 25, 2006
5. 