Pattern, Gun aur ek Pyaari Vidhi!

Class 7 Maths · Chapter 11: Saajha Aadhaar Dhoondhna · NCERT Ganita Prakash section P2 3.3

Seekho

Aam kathan: 6 aur 18 ka HCF 6, kyunki 6, 18 ka factor hai. Aam taur par n aur 5n ka HCF n: "mera factor bano, main tumhara multiple!" Do lagaataar numbers ka HCF 1; do lagaataar even ka 2. HCF 1 wale numbers co-prime hain, aur unka LCM unka guna.

HCF(n, 5n) = n

Dono numbers double karne par HCF double: 270 aur 50 ka HCF 10, jabki 540 aur 100 ka 20 (har ek mein ek aur 2). Ek hi number ke multiples: 14 × 6 aur 14 × 9 ka HCF 14 × 3 = 42, sirf 14 nahi, kyunki 6 aur 9 mein 3 saajha.

HCF(14 × 6, 14 × 9) = 42

Pyaari vidhi: dono numbers ko baar-baar common prime se bhaag do: 84, 180 → 42, 90 → 21, 45 → 7, 15 (koi common prime nahi bacha). HCF = 2 × 2 × 3 = 12, baayein ke bhaajak. LCM = bhaajak × aakhri pankti: 12 × 7 × 15 = 1260. Kisi bhi kadam par koi bhi common factor chalta hai, jaise 630, 770 ko pehle 10 se.

HCF = 12 · LCM = 12 × 7 × 15 = 1260

HCF × LCM = guna. 105 = 3 × 5 × 7 aur 95 = 5 × 19: LCM = 3 × 5 × 7 × 19, HCF = 5, aur 105 × 95 = LCM × 5. Saajhe primes ek baar HCF mein aur ek baar LCM mein; baaki LCM mein. To LCM kabhi guna se zyaada nahi.

HCF × LCM = a × b

Explore: co-prime jodiyan.

1. Jodiyan sort karo: kya HCF 1 hai?

Yaad rakho

• Lagaataar numbers co-prime; co-prime numbers ka LCM unka guna.
• HCF × LCM = dono numbers ka guna.

Quick check

Do numbers ka HCF 6 aur LCM 180. Ek 36 hai. Doosra?

1. 30
2. 6
3. 180
4. 216

Socho

3, 4, 5 aur 7 se bhaag hone wala sabse chhota number jo 11 se bhaag par 10 shesh de.

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.