Lagnever AI English

Co-prime numbers kya hote hain?

Short mein jawab

Do numbers co-prime hain agar unka akela common factor 1 ho. Jaise 4 aur 9 co-prime hain, par 15 aur 39 nahi, kyunki dono 3 se divisible hain. Co-prime numbers ka khud prime hona zaroori nahi. Jaanchne ke liye prime factorisation nikaalo: agar dono mein koi prime factor common nahi, to wo co-prime hain.

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Khazaana game mein common factors

Jump Jackpot game mein Jumpy 0 se shuru karke ek tay size ki chhalaang lagaata hai; khazaane par utarne par wo jeetta hai. Do khazaanon par utarne ke liye jump size dono numbers ka factor hona chahiye, yaani common factor. 28 aur 70 par rakhe khazaanon ke liye kaam karne waale jump size 1, 2, 7 aur 14 hain.

0 se 70 tak number line par 14 ki chhalaang 28 aur 70 dono par utarti hai, jabki 4 ki chhalaang 28 par utarti hai par 70 par nahi; kaam karne waale jump size common factors 1, 2, 7 aur 14 hain
28 aur 70 par khazaane

Surakshit jode aur co-prime numbers

Ab naya niyam: 1 ki chhalaang mana hai. Grumpy do khazaane aise rakhna chaahta hai ki Jumpy dono tak na pahunch sake. 12 aur 26 par rakhna kaam nahi karta, kyunki 2 ki chhalaang dono tak pahunchti hai. Par 4 aur 9 surakshit hain: 1 ke alawa koi jump size dono tak nahi pahunchta.

Surakshit jodon ka 1 ke alawa koi common factor nahi hota. Aise numbers ko co-prime kehte hain. Book ke jode jaanchein:

JodaCo-prime?
15 aur 39Nahi: common factor 3
4 aur 15Haan
18 aur 29Haan
20 aur 55Nahi: common factor 5
18 aur 35Haan
30 aur 415Nahi: common factor 5
17 aur 69Haan (69 = 3 × 23)
81 aur 18Nahi: common factor 9

Co-prime ka matlab prime nahi

Co-prime numbers ke ek jode ke baare mein hai. Numbers khud composite ho sakte hain: 4 = 2 × 2 aur 9 = 3 × 3 ka 1 ke alawa koi common factor nahi, isliye wo co-prime hain. Do alag primes hamesha co-prime hote hain, kyunki har ek ke factors sirf 1 aur khud hain.

Prime factorisation se jaanch

Ek factor joda kaafi nahi. Anshu ne 56 = 14 × 4 aur 63 = 21 × 3 likha, koi common factor nahi dekha aur galti se kaha ki wo co-prime hain; Guna ne 56 = 7 × 8 aur 63 = 9 × 7 likhkar 7 dhoondh liya. Pakka tareeka poori prime factorisation hai:

  • 56 = 2 × 2 × 2 × 7 aur 63 = 3 × 3 × 7 mein prime 7 common hai, isliye wo co-prime nahi.
  • 40 = 2 × 2 × 2 × 5 aur 231 = 3 × 7 × 11 mein koi prime common nahi, isliye wo co-prime hain.
  • 242 = 2 × 11 × 11 aur 195 = 3 × 5 × 13 mein koi prime common nahi, isliye wo co-prime hain.

Agar do numbers ka koi composite common factor hota, to uske prime factors dono factorisations mein aate, isliye koi common prime nahi matlab 1 ke alawa koi common factor nahi.

Pehla common multiple

Idli-vada game mein Anshu ne dekha ki do numbers ka pehla common multiple kabhi unke guna ke barabar hota hai aur kabhi usse chhota. Co-prime jodon ke liye ye guna ke barabar hai: 4 aur 9 pehli baar 36 = 4 × 9 par milte hain, aur 3 aur 5, 15 par. Jab numbers ka koi factor common ho, to ye chhota hota hai: 4 aur 6 pehli baar 12 par milte hain, 24 par nahi, aur 6 aur 8, 24 par, 48 par nahi.

Co-prime thread art

Kheelon (pegs) ke ek gole par dhaaga baandho, har baar tay ginti ki kheelein chhodkar. Dhaaga har kheel tak tabhi pahunchta hai jab kheelon ki ginti aur thread-gap co-prime hon.

Thread art: 15 kheelein aur gap 10 sirf 3 kheelein use karte hain, 10 kheelein aur gap 7 saari 10, 14 kheelein aur gap 6 sirf 7, aur 8 kheelein aur gap 3 saari 8
Co-prime thread art

Numbers ko primes mein todne ke liye padho prime factorisation kaise karein. Textbook ke sawaalon ke liye dekho Chapter 5 ke NCERT solutions; poore chapter ke liye Chapter 5 ke notes.

Practice karo

  1. Kaunsa joda co-prime hai?

    1. (a) 15 aur 39
    2. (b) 20 aur 55
    3. (c) 18 aur 29
    4. (d) 30 aur 45
    Jawab dekho

    Jawab: (c) 18 aur 29

  2. Kaunsa joda co-prime NAHI hai?

    1. (a) 4 aur 15
    2. (b) 17 aur 69
    3. (c) 57 aur 85
    4. (d) 121 aur 1331
    Jawab dekho

    Jawab: (d) 121 aur 1331

  3. Kis jode ka pehla common multiple unke guna ke barabar hai?

    1. (a) 4 aur 6
    2. (b) 6 aur 8
    3. (c) 4 aur 9
    4. (d) 10 aur 15
    Jawab dekho

    Jawab: (c) 4 aur 9

  4. Kya 80 aur 63 co-prime hain? Prime factorisation se batao.

    Jawab dekho

    Jawab: Haan. 80 = 2 × 2 × 2 × 2 × 5 aur 63 = 3 × 3 × 7 mein koi prime factor common nahi, isliye unka akela common factor 1 hai.

  5. Kya koi bhi do prime numbers co-prime hote hain?

    Jawab dekho

    Jawab: Haan, agar wo alag hon: har ek ke factors sirf 1 aur khud hain, isliye common factor sirf 1 hai. (Prime apne aap se co-prime nahi: 5 aur 5 ka common factor 5 hai.)

Students ke sawal

Co-prime numbers kya hote hain?

Do numbers jinka 1 ke alawa koi common factor na ho, jaise 4 aur 9, 8 aur 15, ya 18 aur 35.

Kya co-prime numbers hamesha prime hote hain?

Nahi. Co-prime ka matlab hai ki do numbers ke jode ka 1 ke alawa koi common factor nahi. Numbers khud composite ho sakte hain, jaise 4 aur 9.

Kaise jaanchein ki do numbers co-prime hain?

Har number ki prime factorisation likho. Agar koi prime dono mein na aaye, to numbers co-prime hain; agar koi prime dono mein aaye, to wo common factor hai aur wo co-prime nahi.

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