Highest common factor (H.C.F) tricks se kaise nikale? hindi

Aap logo ne multiplication k tricks k bahot post pade. Par is post me mai kuch naya tricks laya hu. Is post me aap Highest common factor ( H.C.F) ya jise Greatest common divisor (G.C.D) bhi kahate hai k tricks janege. Ise hindi me म 0 स0 kahate hai. म0 स0 ka matlab"mahtam samapwartak" (महत्तम समापर्वतक ) hota hai. Hum samikarado(Equations)  ka " Highest common factor " tricks k saath nikalana janege. Ab aage ki line me mai " Highest common factor " ko " H.C.F Kahuga. To chaliye start karte hai -:
Aaj ka topic hai ki -:

Highest common factor (H.C.F) k sawalo ko shortcuts ya tricks se kaise karte hai ?

Example -1. Maan lete hai ki hume X^2 + 7x + 6 aor X^2 - 5x - 6 ka H.C.F. nikalana hai. 

Full solution -: Iss example ko jab samanya tarike (general method ) se karna ho to aise 

                           karege -:

Sabse phale dono samikarano ( equation ) ka gudankhand ( factor ) nikalte hai -:

X^2 + 7x + 6 = x^2 + (6+1)x + 6

                       = x^2 + 6x + 1x + 6

                       = x(x+6) + 1 (x+6)

                       = (x+1)(x+6)

 Ab dusre ka gudankhand nikale -:

X^2 - 5x - 6 = x^2 - (6 - 1)x - 6

                    = x^2 - 6x + 1x - 6

                    = x(x - 6) +1(x - 6)

                    = (x + 1)(x - 6)

Ab dono ka gudankhand krmsh (x+1)(x+6) aor (x+1)(x-1) hai. 

Phir dono samikarno k gudankhad k common factor ko dono samikarno ka H.C.F hota hai. 

Yaha dono samikarano ka common factor "( x + 1)" hai. Iss liye 

X^2 +7x + 6 aor x^2 - 5x - 6 ka H.C.F = ( X + 1 )   Answer. 

Ab issi example ko tricks ya shortcut se dekh -:

Tricks -: Tricks se karne k liye aap dono samikarano ko jode ya ghataye jaisa Maine niche
                 Kiya hai -:
                 (1) jodane ( add ) karne par -:
                                                                    X^2 + 7x + 6
                                                                    X^2 -  5x -  6      
                                                                    2x^2 + 2x            
                 Dono samikarano ko jodane par " 2x^2 + 2x" aaya. Ab isme se "2x" common lenge. To.
                 " 2x ( x +1) "  common lene k baad jo aaya " ( x + 1)" in dono samikarno ka H.C.F
               hoga.
               (x^2 + 7x + 6 )  aor (x^2 - 5x - 6) ka H.C.F = (x + 1) Answer. 
To dekha aapne tricks se karne par ye example kitana aasan aor jaldi se ho gaya.  
            (2) Ghatane ( minus) karne par -:
            Samikarno ko aise likhe -:
                               X^2 + 7x + 6
                               X^2 - 5x -  6     
                                      12x +12    
Minus karne par " 12x + 12 " mila ab isme se 12 ko common lenge. Common lene k baad hume " (x + 1) " milta hai. Yahi "(x+1) " dono samikarno ka H.C.F. hai.
To
     (x^2 + 7x + 6 ) aor (x^2 - 5x -6) ka H. C. F.  = ( x+1) Answer.
To dekha aapne aap add kark ya subtract dono me se kisi bhi ek method ka use kark aap
H. C. F. nikal sakte hai.
Aapko ye post kaisi lagi aagar aapko ye post se related aor example chahiye to hume comments kare. Aagar aapko mathematics me koi bhi problem ho to jarur puche.