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Class 6 Maths Chapter 5: Prime Time (Hinglish Notes)

Ye chapter 5 lines mein

Prime Time factors aur multiples ke baare mein hai. Jo numbers do numbers ke multiple hon, wo unke common multiples hain, aur jo dono ko poora divide karein, wo unke common factors. Prime number ke theek do factors hote hain, 1 aur khud; composite ke usse zyada; aur 1 dono mein se kuch nahi. Jin do numbers ka 1 ke alawa koi common factor nahi, wo co-prime hain. 1 se bada har number sirf ek tareeke se primes ka guna hai, yaani uski prime factorisation, aur aasaan tests 2, 4, 5, 8 aur 10 se divisibility jaanchte hain.

Chapter 5 ka mind map: common multiples aur factors, prime aur composite numbers, Sieve of Eratosthenes, co-prime numbers, prime factorisation, aur divisibility tests
Poora chapter ek page par

Common multiples aur common factors

Idli-vada game mein bachche baari-baari ginte hain, par 3 ke multiples par ‘idli’, 5 ke multiples par ‘vada’ aur dono ke multiples par ‘idli-vada’ bolte hain. ‘Idli-vada’ numbers, 15, 30, 45, …, 3 aur 5 ke common multiples hain; ye 15 ke multiples hain, isliye 10va 150 hai.

60 tak idli-vada game ka Venn diagram: sirf 3 ke multiples, sirf 5 ke multiples, aur common multiples 15, 30, 45 aur 60
60 tak idli-vada

Jump Jackpot game mein Jumpy 0 se shuru karke ek tay size ki chhalaang lagaata hai. Wo 24 par 1, 2, 3, 4, 6, 8, 12 aur 24 ki chhalaang se pahunchta hai, jo 24 ke factors hain. Do khazaanon, jaise 14 aur 36, tak pahunchne ke liye jump size dono ka common factor hona chahiye: 1 ya 2.

Prime aur composite numbers

Guna 12 anjeer ko kai tarah ke aayaton (rectangles) mein laga sakti hai (1 × 12, 2 × 6, 3 × 4), par Anshu 7 anjeer sirf 1 × 7 mein laga sakta hai. Jis number ke theek do factors hon, 1 aur khud, wo prime number hai; jiske do se zyada factors hon, wo composite number hai. Number 1 ka sirf ek factor hai, isliye wo dono nahi. Pehle primes 2, 3, 5, 7, 11, 13, 17 aur 19 hain, aur 2 akela even prime hai. Aur padho prime aur composite numbers mein.

Sieve of Eratosthenes, lagbhag 2200 saal pehle ke ek Greek ganitagya ke naam par, primes dhoondhta hai: 1 ko kaato, 2 par gola lagaao aur uske multiples kaato, 3 par gola lagaao aur uske multiples kaato, aur aise hi aage. Gole waale numbers prime hain; 100 tak aise 25 hain.

1 se 100 tak Sieve of Eratosthenes: 25 primes par gola, aur composite numbers 2, 3, 5 ya 7 ke multiples ke roop mein kate hue
Sieve of Eratosthenes

Co-prime numbers

Naye khazaana game mein 1 ki chhalaang mana hai. Grumpy ke khazaane 4 aur 9 par surakshit hain, kyunki 1 ke alawa koi jump size dono tak nahi pahunchta. Jin do numbers ka 1 ke alawa koi common factor nahi, wo co-prime hain: 4 aur 9 co-prime hain, par 15 aur 39 ka common factor 3 hai. Co-prime numbers ka pehla common multiple unka guna hota hai. Thread art mein dhaaga har kheel (peg) tak tabhi pahunchta hai jab kheelon ki ginti aur thread-gap co-prime hon. Aur padho co-prime numbers mein.

Prime factorisation

56 aur 63 co-prime hain ya nahi, ye jaanchne ke liye Anshu 56 = 14 × 4 aur 63 = 21 × 3 likhkar galti se kehta hai ki hain, par Guna 56 = 7 × 8 aur 63 = 9 × 7 likhkar common factor 7 dhoondh leti hai. Pakka tareeka hai har number ko primes mein todna: 56 = 2 × 2 × 2 × 7 aur 63 = 3 × 3 × 7. Ise prime factorisation kehte hain. 1 se bade har number ki theek ek hoti hai, factors ke kram ko chhodkar, aur kram se farq nahi padta kyunki guna kisi bhi kram mein kar sakte hain. Aur padho prime factorisation kaise karein mein.

Factor trees: 36 ko 4 × 9 aur 6 × 6 dono tarah todne par wahi primes milte hain, 2 × 2 × 3 × 3, aur 56 = 2 × 2 × 2 × 7
Factor trees

Prime factorisation do sawaalon ka jawab deti hai. Do numbers co-prime hain agar unme koi prime factor common na ho, jaise 40 = 2 × 2 × 2 × 5 aur 231 = 3 × 7 × 11. Ek number doosre ko divide karta hai agar uski prime factorisation doosre mein shaamil ho: 168 = 2 × 2 × 2 × 3 × 7, 12 = 2 × 2 × 3 se divisible hai, par 42 = 2 × 3 × 7 nahi, kyunki usme sirf ek 2 hai.

Divisibility tests

Har baar lamba bhaag zaroori nahi. Koi number 10 se divisible hai agar aakhri ank 0 ho, 5 se agar 0 ya 5 ho, aur 2 se agar 0, 2, 4, 6 ya 8 ho. 4 ke liye aakhri do ank dekho, aur 8 ke liye aakhri teen, kyunki 100, 4 ka multiple hai aur 1000, 8 ka. Isliye 8560, 2, 4, 5, 8 aur 10 sabse divisible hai. Aur padho divisibility ke rules mein.

Numbers ke saath mazaa

Chaar numbers ke ek box mein har number apne tareeke se khaas ho sakta hai: jaise 9, 16, 25 aur 43 mein 9 akela ek ank waala number hai aur 43 akela prime. Prime puzzle mein grid ko primes se aise bharte hain ki har row aur column ka guna diye gaye number ke barabar ho.

Har sawaal ka jawab Chapter 5 ke NCERT solutions mein hai.

Key terms (zaroori shabd)

TermMatlab
Factor (gunankhand)Wo number jo kisi doosre number ko poora divide kare: 4, 12 ka factor hai kyunki 12 ÷ 4 = 3.
Multiple (gunaj)Kisi number ko 1, 2, 3, … se guna karke mila number: 3, 6, 9 aur 12, 3 ke multiples hain.
Common multipleWo number jo do ya zyada numbers ka multiple ho: 15, 30 aur 45, 3 aur 5 ke common multiples hain.
Common factorWo number jo do ya zyada numbers ka factor ho: 1 aur 2, 14 aur 36 ke common factors hain.
Prime numberWo number jiske theek do factors hon, 1 aur khud, jaise 2, 3, 5, 7, 11 aur 13.
Composite numberDo se zyada factors waala number, jaise 4, 6, 8, 9 aur 10; number 1 na prime hai na composite.
Sieve of EratosthenesPrimes nikaalne ka tareeka: 1 ko kaato, phir har prime ke multiples baari-baari kaato; jo bachte hain wo prime hain.
Twin primesPrimes ke jode jinka farq 2 ho, jaise 3 aur 5, 11 aur 13, ya 17 aur 19.
Co-prime numbersDo numbers jinka 1 ke alawa koi common factor na ho, jaise 4 aur 9.
Prime factorisationNumber ko primes ke guna ke roop mein likhna, jaise 56 = 2 × 2 × 2 × 7; 1 se bade har number ki sirf ek hoti hai, kram ko chhodkar.
Perfect numberWo number jiske factors ka jod number ka dugna ho, jaise 6 (1 + 2 + 3 + 6 = 12) aur 28.
Divisibility testBina lambe bhaag ke jaanchne ka aasaan tareeka ki koi number kisi doosre se divide hota hai ya nahi, jaise 10 ke liye aakhri ank 0.

Is chapter ke topics

Is chapter ke NCERT solutions Chapter ke saare exercise questions, step-by-step jawab ke saath.

Practice karo

  1. Inme se prime number kaunsa hai?

    1. (a) 51
    2. (b) 57
    3. (c) 37
    4. (d) 91
    Jawab dekho

    Jawab: (c) 37

  2. Kaunsa joda co-prime hai?

    1. (a) 15 aur 39
    2. (b) 18 aur 35
    3. (c) 30 aur 415
    4. (d) 81 aur 18
    Jawab dekho

    Jawab: (b) 18 aur 35

  3. 72 ki prime factorisation kya hai?

    1. (a) 2 × 2 × 3 × 6
    2. (b) 2 × 2 × 2 × 3 × 3
    3. (c) 8 × 9
    4. (d) 2 × 3 × 12
    Jawab dekho

    Jawab: (b) 2 × 2 × 2 × 3 × 3

  4. 8536, 4 se divisible kyun hai?

    1. (a) kyunki ye 6 par khatm hota hai
    2. (b) kyunki 36, 4 ka multiple hai
    3. (c) kyunki ye even hai
    4. (d) kyunki 8 + 5 + 3 + 6 = 22
    Jawab dekho

    Jawab: (b) kyunki 36, 4 ka multiple hai

  5. 3 aur 5 waale idli-vada game mein ‘idli-vada’ 10vi baar kis number par bola jaata hai?

    1. (a) 50
    2. (b) 100
    3. (c) 150
    4. (d) 300
    Jawab dekho

    Jawab: (c) 150

Students ke sawal

Class 6 Maths Chapter 5 ke main topics kya hain?

Idli-vada aur khazaana games se common multiples aur common factors, prime aur composite numbers, Sieve of Eratosthenes, co-prime numbers, prime factorisation, 2, 4, 5, 8 aur 10 ke divisibility tests, aur number puzzles.

Kya Prime Time nayi Ganita Prakash book mein hai?

Haan. Prime Time, Class 6 Maths ki textbook Ganita Prakash (Reprint 2026-27) ka Chapter 5 hai. Ye Chapter 4, Data Handling and Presentation, ke baad aata hai.

Chapter 5 mein kitne sawaal hain?

Paanch Figure it Out sets hain, jinme 10, 12, 5, 4 aur 7 sawaal hain, saath mein Math Talk aur Try This ke sawaal aur prime puzzles. Hamara NCERT solutions page har ek ka jawab deta hai.

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