I'm a professional game developer from Wakefield, England, working as a senior programmer for Rebellion North.
I'm a married father of five and I a also sometimes do Retroburn stuff.
Martin 'Bytrix' Caine
Father. C++ Games Programmer. Cyclist. Guitarist.
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Monday, May 31st 2010 / Web

Project Euler - problem 3

The third problem from Project Euler was a little more complex:

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143

I split this in to two processes. First I calculated the factors of 600851475143, I then ordered them in reverse order.

I then tested each factor to see if it was prime by incrementing from 2 to the value of the factor while testing the division by the variable. If a division resulted in a whole number then the factor is not prime and we move onto the next factor.

I'm sure there are more efficient ways to determine whether a value is prime (simple only testing division by primes would be an option).

The program returns when we find a prime number among the factors:

*  ProjectEuler.net  *  Problem 3  *  2010-05-31  *  Martin Caine *

//The prime factors of 13195 are 5, 7, 13 and 29.
//What is the largest prime factor of the number 600851475143 ?

$total 0;

// create an array to store the factors of 600851475143
$factors = array();

// we won't ever hit 600851475143 as we'll break well before then
for( $i 2$i<600851475143$i++ )
// check to see if dividing by this returns a whole number
$result 600851475143/$i;
$result == (int)$result )
// if this is in our array we have found all the factors
if( in_array$i$factors ) )
$factors[] = $result;
$factors[] = $i;

// sort factors with largest first
rsort$factors );

// loop through factors
foreach( $factors as $factor )
// by default, assume prime, we mark as not being prime in the loop
$isPrime true;
$i=2$i<$factor$i++ )
$result $factor/$i;
$result == (int)$result )
// we found a factor so it's not prime
$isPrime false;
$isPrime )
// we found our prime, and we're testing largest first so output and die
echo $factor;

'no prime factor found';


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Tags:   php   project euler   web