Created
December 5, 2010 18:13
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largest_prime_factor
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<?php | |
test(); | |
/** | |
* The largest prime factor | |
* | |
* The provided number is not considered a factor of itself. | |
* | |
* @param int $n The number we wish to find a factor of | |
* @return int|false false is returned when there are no prime factors | |
*/ | |
function largest_prime_factor($n) | |
{ | |
$limit = floor(sqrt($n)); | |
$lpx = false; // Largest prime x | |
for ($x = 2; $x <= $limit; $x++) | |
{ | |
$y = $n / $x; | |
if (is_int($y) && is_prime($y)) { | |
return $y; | |
} | |
if (is_prime($x)) { | |
$lpx = $x; | |
} | |
} | |
return $lpx; | |
} | |
/** | |
* All factors of a number | |
* | |
* Note that when there are an odd number of factors returned, $n is a square | |
* number and the last factor is the square root. | |
* | |
* @param int $n | |
* @return array | |
*/ | |
function factors($n) | |
{ | |
$limit = sqrt($n); | |
$factors = array(); | |
for ($x = 2; $x <= $limit; $x++) | |
{ | |
$y = $n / $x; | |
if (is_int($y)) { | |
$factors[] = $x; | |
if ($x != $y) $factors[] = $y; | |
} | |
} | |
return $factors; | |
} | |
/** | |
* Whether a number is prime or not | |
* | |
* @param int $n The number in question | |
* @param bool | |
*/ | |
function is_prime($n) | |
{ | |
if ($n < 4) return true; | |
$limit = sqrt($n); | |
// Check if the square root is a factor | |
// -- if it is, $n is not prime | |
if (is_int($limit)) | |
return false; | |
// Check the lower components of pairs of factors | |
// -- if any exist, $n is not prime | |
for ($x = 2; $x <= $limit; $x++) | |
if (($n % $x) == 0) | |
return false; | |
// Otherwise, $n is prime | |
return true; | |
} | |
function test() | |
{ | |
header("Content-Type: text/plain"); | |
echo "Key: !sqrt >lpf\n\n"; | |
for ($n = 1; $n < 40; $n++) | |
{ | |
$factors = factors($n); | |
sort($factors); | |
$sqrt = sqrt($n); | |
$lpf = largest_prime_factor($n); | |
$factors = array_map(function($f) use($sqrt, $lpf) { | |
if ($f == $sqrt) { | |
if ($f == $lpf) { | |
return '!>'.$f; | |
} | |
return '!'.$f; | |
} else if ($f == $lpf) { | |
return '>'.$f; | |
} | |
return $f; | |
}, $factors); | |
echo $n, ': [', implode(', ', $factors) ,"]\n"; | |
} | |
} |
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