hn^, ffYa]nT gj hn, Phn b GnIljalfhlPkf]\J _jdhlJ aJ`l VnZhfZ
bfh\_jhQ, lVn ^nW\h _nfak`nbjhQ nfanKgkglZ gj djVnhk l `d\Wlk gk-
_dlZhgnfhl. 8h`kaQgYk hj]lk ;j]hY kfhQ, gn @hn gk ^nKkh fa\KlhQ
n_djb`jglk^ fbnkT VkX`kZhkaQgnfhl. 8V @hn^ fbl`khkaQfhb\Jh l dk-
X\aQhjhY WnanfnbjglZ gj bYVndjO b ^kfhgYk fj^n\_djbakglZ. j ]jg-
`l`jhnb b `k_\hjhY nh GCD (_n`P>d]lbjJ – l^kggn nh GCD), j gk
hnaQ]n nh bfkWn f_lf]j nV#k`lgkglZ «kghd fnWajflZ», _dnWnanfn-
bjan gjlVnaQHkk Xj bfJ lfhndlJ bYVndnb b gkXjblfl^nT Djhbll
Plfan lXVldjhkakT. j gjHlO ]jg`l`jhnb aJ`l _dnWnanfnbjal `jKk
b hj]lO dkWlngjO, W`k gkh gjHlO _kdblPgYO _jdhlTgYO ndWjglXjIlT,
gj_dl^kd, BlaZgf]lT ]djT. 1jX\^kkhfZ, hjTgnk Wnanfnbjglk gj bY-
VndjO l bfh\_akglk b GnIljalfhlPkf]\J _jdhlJ f _nfak`\JEl^l j]-
hlbgY^l `kTfhblZ^l b fnnhbkhfhbll f _dnWdj^^nT _jdhll – @hn
gkf]naQ]n djXgYk bkEl. 4n flh\jIlZ _n`hbkdK`jkh, Phn gjHlO fhn-
dnggl]nb WndjX`n VnaQHk, Pk^ ^Y f\^kal _dlnVElhQ ] _jdhll ]j] ]
_nalhlPkf]nT ndWjglXjIll. !hn _n`hbkdK`jkh n_Yh dZ`j _kdblPgYO
ndWjglXjIlT gjHkT _jdhll: «kghdjaQgjZ» (fk]dkhjdQ hnb. 1n`ln-
gnb 2.), DjhWjaQf]nWn _dk`^kfhQZ W.1lWl (VYbHjZ «.kgWjdjWf», fk]dk-
hjdQ hnb.1YKgl]nb 4.), «D\`Xj» (fk]dkhjdQ hnb n]lH .), «.djfajbj»
(fk]dkhjdQ hnb. BjflaQkb +.), «1kXk]gk» (fk]dkhjdQ hnb. -Vdj^nbj 2.).
Cn]j gk\`nbakhbndlhkaQgn bk`>hfZ djVnhj _n fnX`jglJ gnbYO
_kdblPgYO ndWjglXjIlT _jdhll. j]hlPkf]l fnX`jgj alHQ n`gj _kd-
blPgjZ ndWjglXjIlZ «Dlk_jZ» (fk]dkhjdQ hnb. kaakd 6.), l bf>.
Cdjbakglk l CnalhlPkf]lT fnbkh GCD gjdZ`\ f fk]dkhjdZ^l
_kdblPgYO ndWjglXjIlT `naKgY _dlXgjhQ `naJ fbnkT nhbkhfhbkg-
gnfhl Xj ^kàkggnk bY_nagkglk dkHkglT f#kX`j.
106 GCD: +G(81+ B 28.*64(-
Cdjbakglk l CnalhlPkf]lT fnbkh GCD djf_dk`kalal bfkO lX-
VdjggYO XI f#kX`n^ Pakgnb l ]jg`l`jhnb b PakgY Cnalhfnbkhj GCD
_n dkWlngj^ dkf_\Val]l l gjXgjPlal nhbkhfhbkggYO b ]jK`nT Wd\__k.
Bfk fnWajflalfQ, gn `jaQHk fnWajflZ `kan gk _nHan. (d\`gn gjThl
nV#k]hlbgYk _dlPlgY lal n_djb`jglk gkbY_nagkggnWn, kfal Wd\__Y
gj djXdjVnh]\ _ajgj fnb^kfhgYÒkTfhblT gk fnVldjalfQ l gj ^kfhn
gk bYkXKjal. 4k _n^nWal lf_djblhQ flh\jIlJ flfhk^jhlPkf]lk gj-
_n^lgjglZ nV @hnT Xj`jPk gj Xjfk`jglZO CdjbakglZ l CnalhlPk-
f]nWn fnbkhj GCD. 4k _nfh\_lan fn fhndngY hnbjdlEkT gl n`gnWn
_dkànKkglZ, ]j] `kTfhbnbjhQ _n-lgn^\, kfal _dkànKkggjZ l fj-
^l^l n`nVdkggjZ ;nd^j djVnhY gk_dlk^ak^j lal gk@;;k]hlbgj.
!hj djVnhj nfhj>hfZ n`gnT lX WajbgkTHlO l gj _dk`fhnZElT Wn`
`n III f#kX`j GCD, ]nhndYT l `jfh _kdfngjaQg\J nIkg]\ hk^, ]hn
gk hnaQ]n gk bY_nagZa, gn l glPkWn gk _dk`_dlgZa àZ bY_nagkglZ
bjKgkTHkWn _jdhlTgnWn _nd\PkglZ.
-gjalXld\Z djVnh\ _n \]dk_akglJ _jdhll gknVOn`l^n nfhjgnblhQ
bgl^jglk `kakWjhnb f#kX`j gj kE> n`gnT _dnVak^k. 1kPQ l`>h n ^j-
anPlfakggYO _jdhlTgYO ndWjglXjIlZO, fnfhnZElO lX _jdhlTIkb b bnX-
djfhk 75 l Vnakk akh. +O gk^gnWn, gn ngl kfhQ. CjdhlTIY-bkhkdjgY,
djX\^kkhfZ, gk blgnbjhY, Phn fnfhjdlalfQ l gk ^nW\h bkfhl Vnakk j]-
hlbg\J djVnh\. +O blgj alHQ b hn^, Phn fbnkbdk^kggn gk _nXjVnhl-
alfQ n fbnkT f^kgk, n _dl>^k b _jdhlJ ^nan`YO. !hn f n`gnT
fhndngY. G `d\WnT fhndngY, l _dj]hl]j @hn _n`hbkdK`jkh, b hj]lk nd-
WjglXjIll Vnakk ^nan`Yk aJ`l gk bfh\_jJh. +^, b_nagk anWlPgn,
hj^ gklghkdkfgn. 6fal `kakWjhY f#kX`j gk bgkf\h `d\WlO _dkànKk-
glT, hn fak`nbjan VY, _n ^gkglJ CdjbakglZ, fnX`jbjhQ _jdjaakaQgn
f\Ekfhb\JEl^ bkhkdjgf]l^ _kdblP]j^, ndWjglXjIll lX Vnakk ^nan-
`YO fhndnggl]nb gj Vnakk j]hlbgnT ndWjglXjIlnggnT l `kZhkaQgnT
nfgnbk, _n` `d\Wl^ gjXbjglk^, h.k. fj^nfhnZhkaQgYk ndWjglXjIll, ]n-
hndYk ^nWal VY fnhd\`glPjhQ f \Kk l^kJEl^lfZ _kdblP]j^l l b
lhnWk nV#k`lglhQfZ _n` gnbY^ l Vnakk ^nan`Y^ d\]nbn`fhbn^.
bkdkg, Phn `kakWjhY f#kX`j f _ngl^jglk^ _n`nT`\h ] nIkg]k fl-
h\jIll b @hnT nVajfhl, bgkf\h l fbnl _dkànKkglZ, j _n bnXbdjEkglJ
`n^nT b _kdblPgYO ndWjglXjIlZO _n^nW\h ndWjglXnbjhQ @h\ djVnh\.
XII G62 GCD 107
Cn`Wnhnb]j l \Pjfhlk b bYVndjO
^kfhgnWn fj^n\_djbakglZ Djhbll
l 6bdn_kTf]nWn _jdaj^kghj
1kHkglZ I f#kX`j GCD b @hnT nVajfhl ^nKgn fPlhjhQ bY_na-
gkggY^l.
4j bYVndjO, ]j] @hn n_dk`kala f#kX` _jdhll, ^Y bYfh\_jal _n
k`lgn^\ f_lf]\ 8V#k`lgkglZ _nalhlPkf]lO ndWjglXjIlT «kghd fn-
WajflZ» l _na\Plal OndnHlT dkX\aQhjh. B ^kfhgYk fj^n\_djbakglZ
VYal lXVdjgY 18 hnbjdlEkT nh GnIljalfhlPkf]nT _jdhll Djhbll l
n`lg Pkanbk] (_dk`fk`jhkaQ GCD) – b `k_\hjhY 6bdn_kTf]nWn _jd-
aj^kghj. 4jHl ]jg`l`jhY fhjal `k_\hjhj^l b 1lWk – 7 Pkanbk]; b
1kXk]gk – 4 Pkanbk]j; b D\`Xkgf]n^ ]djk – 2 Pkanbk]j; b -a\]fgkg-
f]n^, BlaZgf]n^, .jdfjbf]n^, la\_f]n^ l 6]jV_laff]n^ ]djZO –
_n n`gn^\ Pkanbk]\.
!hn gkfn^gkggYT \f_kO _n fdjbgkglJ fn bfk^l _dk`Y`\El^l
bYVndj^l. +XVdjglk gjHlO hnbjdlEkT VYan nVkf_kPkgn _djblaQ-
gnT _dk`bYVndgnT hj]hl]nT – ^Y Hal b k`lgn^ f_lf]k «kghdj fn-
WajflZ» b \fanblZO dnfhj `nbkdlZ ] akbY^ l akbn-Ikghdlfhf]l^
flaj^ b Djhbll, j hj]Kk VajWn`jdZ \^kan _nfhdnkggnT _dk`bYVnd-
gnT ]j^_jgll, _nfhdnkggnT b nfgnbk gj alPgn^ nVEkgll f lXVldj-
hkaZ^l, h.]. fdk`fhb gj lf_naQXnbjglk hkakbl`kglZ, dj`ln,