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Is there an easy way to determine how many factors a number has?



#9

My student wanted to know. The classic way is to do the prime factorization for the number, take the exponent of each prime factor and add 1 to it and multiply these together, and the result is the number of factors that the original number has.

The 17b can do it easily in a solver equation:

nf=0xL(a:(n))+2+(i:2:g(a):1:if(mod(n:i)=0:if(i=a:1:2):0))

It works on the 17b, 17bii, and 17bii+, although it's much slower on the plus.


Edited: 2 July 2011, 9:45 p.m.


#10

I'm not aware of any and I believe that finding this is equivalent in difficult to factorising. I looked at adding this to the 34s firmware but didn't dig too deeply.

Once you have the prime factorisation, determining the factors is straightforward as you've pointed out.


- Pauli

#11

Otherwise there would be a an easy way to tell whether a number is prime or not. There are a number of interesting properties related to this, however. One of them states that perfect squares, and only them, have an odd number of divisors (more at OEIS). This is the basis for the optimized solution to the 100 doors problem (the following wp34s program will display the doors that will be open after the last pass).

001 LBL D
002 2
003 10^x
004 SQRT
005 FP?
006 SKIP 02
007 RCL L
008 PSE 10
009 DEC L
010 x<> L
011 x>1?
012 BACK 08
013 RTN

#12

Gerson, wouldn't it be much easier to just compute the squares from 1^2 to 10^2 instead of testing each integer if it is a square?


#13

Yes, it would :-) And it would make for an extremely short wp34s program.

BTW at least a couple of optimized C solutions there follow that approach:

#include <stdio.h>

int main()
{
int i;
for (i = 1; i * i <= 100; i++)
printf("door %d open\n", i * i);

return 0;
}

#include <iostream> //compiled with "Dev-C++" , from RaptorOne

int main()
{
for(int i=1; i*i<=100; i++)
std::cout<<"Door "<<i*i<<" is open!"<<std::endl;
}

A mathematical explanation, in Spanish:

http://gaussianos.com/el-problema-de-las-100-puertas-y-los-divisores-de-un-numero-natural/


Edited: 3 July 2011, 2:36 p.m.


#14

at last an explanation I can understand :-)

#15

lol... in RPL could be

"door " { 1 2 3 4 5 6 7 8 9 10 } SQ ADD " is open" ADD MSGBOX

#16

On the 50G it's very easy, but it's a little cheating ;)

DIVIS SIZE


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