ȸ¿ø°¡ÀԡžÆÀ̵ð/ºñ¹øã±â
ȨÀ¸·Î

ÃÖ´ë°ø¾à¼ö ±¸Çϱâ (À¯Å¬¸®µå ¾Ë°í¸®Áò)
13³â Àü
µÎ¼ö »çÀÌ¿¡ ÃÖ´ë°ø¾à¼ö°¡ Á¸ÀçÇÑ´Ù¸é,
$A¿Í $B »çÀÌ¿¡´Â ÃÖ´ë°ø¾à¼ö $G¸¦ °¡Áö´Â ¼ö½ÄÀÌ ¿Ï¼ºµÈ´Ù.

ÀμöºÐÇØ

$A = $G * $x  
----- 1½Ä
$B = $G * $y  ----- 2½Ä
  


1½Ä°ú 2½ÄÀ» ´Ù½Ã Ç¥ÇöÇϸé,

$A - $B = ($G * $x) - ($G *$y) = $G * ($x - $y) ----- 3
½Ä
$A % $B = ($G * $x) % ($G *$y) = $G * ($x % $y) ----- 4½Ä
  


3½Ä¿¡¼­, $A¿Í $B°¡ ÃÖ´ë°ø¾à¼ö¸¦ °¡Áö¸é, $A-$Bµµ $A¿Í $B°¡ °¡Áö´Â ÃÖ
´ë°ø¾à¼ö¸¦ °°ÀÌ °°´Â´Ù.
$G = GCD($A, $B) = GCD($A - $B, $B)  = GCD($B, $A)

4½Ä¿¡¼­, $A¿Í $B°¡ ÃÖ´ë°ø¾à¼ö¸¦ °¡Áö¸é, $A%$Bµµ $A¿Í $B°¡ °¡Áö´Â
ÃÖ´ë°ø¾à¼ö¸¦ °°ÀÌ °°´Â´Ù.
$G = GCD($A, $B) = GCD($A % $B, $B)  = GCD($B, $A)

Áï, $G = GCD($A, 0) = $A °¡ ¼º¸³µÇ´Â °ÍÀÌ´Ù. ( 0Àº ¾î¶²¼ö¿Í °ö
Çصµ 0À̱⠶§¹®)


<?php
function get_cgd($u, $v)  
{  
    $t = 0;  

    while($v) {  
        $t = $u % $v;
      
$u = $v;  
        $v = $t;
    }  
    return $u;  
}
?>

echo get_cgd(45, 10);
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