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POWhat is the best way to get all the divisors of a number?
 

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  1. POWhat is the best way to get all the divisors of a number?
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    <p>Here's the very dumb way:</p> <pre><code>def divisorGenerator(n): for i in xrange(1,n/2+1): if n%i == 0: yield i yield n </code></pre> <p>The result I'd like to get is similar to this one, but I'd like a smarter algorithm (this one it's too much slow and dumb :-)</p> <p>I can find prime factors and their multiplicity fast enough. I've an generator that generates factor in this way:</p> <p>(factor1, multiplicity1)<br> (factor2, multiplicity2)<br> (factor3, multiplicity3)<br> and so on...</p> <p>i.e. the output of </p> <pre><code>for i in factorGenerator(100): print i </code></pre> <p>is:</p> <pre><code>(2, 2) (5, 2) </code></pre> <p>I don't know how much is this useful for what I want to do (I coded it for other problems), anyway I'd like a smarter way to make</p> <pre><code>for i in divisorGen(100): print i </code></pre> <p>output this:</p> <pre><code>1 2 4 5 10 20 25 50 100 </code></pre> <hr> <p><strong>UPDATE:</strong> Many thanks to Greg Hewgill and his "smart way" :) Calculating all divisors of 100000000 took 0.01s with his way against the 39s that the dumb way took on my machine, very cool :D</p> <p><strong>UPDATE 2:</strong> Stop saying this is a duplicate of <a href="https://stackoverflow.com/questions/110344/algorithm-to-calculate-the-number-of-divisors-of-a-given-number">this</a> post. Calculating the number of divisor of a given number doesn't need to calculate all the divisors. It's a different problem, if you think it's not then look for "Divisor function" on wikipedia. Read the questions and the answer before posting, if you do not understand what is the topic just don't add not useful and already given answers.</p>
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    1. USAndrea Ambu
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    1. COThe reason that it was suggested that this question was almost a duplicate of the "Algorithm to calculate the number of divisors of a given number" was that the suggested first step in that question was to _find all of the divisors_, which I believe is exactly what you were trying to do?
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      1. USAndrew Edgecombe
    2. COAndrew in order to find how many divisors there are you simply have to find the prime factors and then use them to count how much divisors there might be. Finding divisors isn't needed in that case.
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      1. USLoïc Faure-Lacroix
 

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