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Prime Factorisation

Class 6 Maths · Chapter 5: Prime Time · NCERT Ganita Prakash section 5.4

Seekho

Har composite number ko prime blocks mein toda ja sakta hai. 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5. Ye 60 ka prime factorisation hai.

Factor tree madad karta hai. 60 ko kaise bhi todo, jaise 6 × 10, phir dobara todo: 6 = 2 × 3 aur 10 = 2 × 5. Aakhir mein phir 2, 2, 3, 5 milte hain. Kaise bhi shuru karo, primes hamesha wahi rehte hain!

Prime factorisation se milaana aasaan hai. 36 = 2 × 2 × 3 × 3 aur 35 = 5 × 7 ka koi prime saajha nahi, to 36 aur 35 co-prime hain. 36 aur 60 mein 2, 2, 3 saajha hain, to 2 × 2 × 3 = 12 unka sabse bada common factor hai.

shared: 2 × 2 × 3 = 12

Explore: factor trees ugao. Jo number prime nahi us par tap karo aur todne ka tareeka chuno.

  1. 60 ko todte raho jab tak har shaakh prime par khatam na ho.
  2. Ab naya tree: 72 ko primes mein todo.

Yaad rakho

  • Prime factorisation: number ko sirf primes ke guna se likho (60 = 2 × 2 × 3 × 5).
  • Kaise bhi todo, wahi primes milte hain. Saajhe primes common factors dikhate hain.

Quick check

24 ka prime factorisation kaunsa hai?

  1. 4 × 6
  2. 2 × 12
  3. 2 × 2 × 2 × 3
  4. 3 × 8
Answer

2 × 2 × 2 × 3. Sirf 2 × 2 × 2 × 3 mein sirf primes hain. 4, 6, 12 aur 8 prime nahi.

Socho

Wo sabse chhota number kaunsa hai jiske prime factorisation mein chaar 2 aur ek 3 ho?

Ek answer

2 × 2 × 2 × 2 × 3 = 48. (Aisa ek hi number hai, isliye wahi sabse chhota bhi hai.)

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.