Woh sabse bada positive integer jo dono numbers ko exactly divide kare.
HCF ke liye prime-factorization rule kya hai?
Har shared prime ko uske dono exponents mein se MINIMUM power pe multiply karo.
LCM ke liye prime-factorization rule kya hai?
Har prime (kisi bhi number se) ko MAXIMUM exponent pe multiply karo.
Euclid's key lemma kya hai?
gcd(a,b)=gcd(b,r) jahan a=bq+r.
Euclid's lemma kyun hold karta hai?
Koi bhi d jo a aur b ko divide kare woh r=a−bq ko bhi divide karega, aur vice versa; same common divisors.
Euclid kab rukta hai aur answer kya hota hai?
Jab remainder=0 ho jaaye; answer last non-zero remainder hota hai.
gcd aur lcm ko link karne wali identity kya hai?
gcd(a,b)·lcm(a,b)=a·b.
Bézout's identity kya hai?
Aise integers x,y exist karte hain jisme ax+by=gcd(a,b).
gcd(360,84)=?
12 (=2²·3).
gcd(a,0)=?
a.
Jin do numbers ka gcd=1 ho unhe kya kehte hain?
Coprime (relatively prime).
Recall Feynman: ek 12-saal ke bacche ko samjhao
Tumhare paas 12 red sweets aur 18 blue sweets hain. Tum identical goodie-bags banana chahte ho jisme SAARI sweets use ho jaayein, har bag mein same red aur same blue. Zyada se zyada kitne bags ban sakte hain? HCF = 6 (har bag mein: 2 red, 3 blue). Aasaan tarike se nikalna ho to: "bada number ko woh bacha lete raho jo chhote number ke baar baar fit hone ke baad bachta hai" — jab kuch nahi bachta tab rukna. Zero se pehle ka last bacha hua number answer hai. Yahi Euclid's algorithm hai.
