Lagnever AI English

Divisibility ke trick aur sabse bada guna

Short mein jawab

Do ankon ke number ab ko 10a + b likhne se uske trick samajh aate hain: ulta number ghataane par 9(a − b) aur jodne par 11(a + b) milta hai. Isi tarah abc + bca + cab = 111(a + b + c). Sabse bada guna banaane ke liye sabse bade ank ko multiplier banaaiye.

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Sabse bada guna

Maan lijiye 2, 3 aur 5 ko ek do ankon wale number guna ek ank wale number mein, har ank ek baar, bharna hai. Pehle dibbe mein teenon mein se koi bhi ank aa sakta hai aur doosre mein bache do mein se koi, isliye 3 × 2 = 6 guna bante hain. Multiplier ke hisaab se lagaane par ye hain 32 × 5 aur 23 × 5, 52 × 3 aur 25 × 3, aur 53 × 2 aur 35 × 2. Ek hi multiplier ke saath bada do ankon wala number jeetta hai, isliye sirf 53 × 2, 52 × 3 aur 32 × 5 bachte hain. Phir 52 × 3, 53 × 2 se aage hai, kyonki wo lagbhag usi number ko bade ank se guna karta hai. 52 × 3 aur 32 × 5 ki tulna ke liye dahaai alag kijiye: 52 × 3 = 150 + 6 aur 32 × 5 = 150 + 10. Dahaai wale hisse barabar hain, isliye 32 × 5 = 160 sabse bada hai.

2, 3 aur 5 se bane chhah guna, multiplier ke hisaab se
2, 3 aur 5 se sabse bada guna

Kisi bhi teen ankon ka niyam

Ank p, q aur r hon, jinmein p sabse chhota aur r sabse bada hai. Har multiplier ke liye bada do ankon wala number jeetta hai, to rq × p, rp × q aur qp × r bachte hain. q, p se bada hai, isliye rp × q, rq × p se bada hai. Baaki do ko kholne par qp × r = 10qr + pr aur rp × q = 10rq + pq milte hain. Dahaai wale hisse barabar hain, aur pr, pq se bada hai kyonki r, q se bada hai. Isliye sabse bada guna qp × r hai: sabse bada ank multiplier hai, aur baaki do ank ghatte kram mein do ankon ka number banaate hain. 4, 6 aur 8 ke liye ye 64 × 8 = 512 deta hai.

Ank ulatkar ghataaiye

Alag-alag ankon wala koi do ankon ka number lijiye, use ulta kijiye, bade mein se chhota ghataaiye aur 9 se bhaag dijiye: kabhi shesh nahi bachta. 82 ke liye 82 − 28 = 54 = 9 × 6. Algebra iski wajah batata hai. Do ankon ka number ab ka maan 10a + b hai, aur uska ulta ba ka maan 10b + a. Agar a bada hai to (10a + b) − (10b + a) = 9a − 9b = 9(a − b); agar b bada hai to antar 9(b − a) hai. Dono haalat mein ye ankon ke antar ka 9 guna hai, aur wahi antar bhaagfal hai: 8 − 2 = 6.

Ank ulatna: antar 9 ka multiple aur jod 11 ka multiple
Ank ulatne par 9 aur 11

Ank ulatkar jodiye

Ghataane ki jagah jodne par 11 saamne aata hai: 82 + 28 = 110, 31 + 13 = 44 aur 47 + 74 = 121. Aam taur par (10a + b) + (10b + a) = 11a + 11b = 11(a + b), isliye jod hamesha ankon ke jod ka 11 guna hota hai.

Teen ankon ke do trick

Teen ankon ka number abc lijiye, jiska maan 100a + 10b + c hai, aur uske ank ghumaakar bca aur cab banaaiye. Teenon ko jodne par 111a + 111b + 111c = 111(a + b + c) milta hai. 111 = 3 × 37 hai, isliye jod hamesha 37 se aur 3 se divisible hota hai: 254 + 542 + 425 = 1221 = 111 × 11.

Ab ankon ko dohraakar chhah ankon ka number abcabc banaaiye. Ye abc × 1000 + abc = abc × 1001 ke barabar hai, aur 1001 = 7 × 11 × 13. Isliye abcabc ko pehle 7, phir 11 aur phir 13 se bhaag dene par hamesha abc waapas milta hai: 254254 ÷ 7 = 36322, 36322 ÷ 11 = 3302 aur 3302 ÷ 13 = 254.

Ank ghumaane par ankon ke jod ka 111 guna; dohraane par 1001 se guna
Teen ankon ke number ke do trick

Ye trick kyon chalte hain

Har trick tabhi tak jaadu lagta hai jab tak ank number ke andar chhupe hain. Sthaan maan khol kar likhne se, 10a + b ya 100a + 10b + c, trick ek chhota hisaab ban jaata hai jismein 9, 11, 111 ya 1001 jaisa gunankhand saaf dikh jaata hai. Numbers ko sthaan maan se likhne ki yahi aadat ankon wali kai doosri paheliyon mein bhi kaam aati hai.

Aur padhein: number socho waale trick, number pyramid aur grid, chapter ke notes aur NCERT solutions.

Practice karo

  1. (93 − 39) ÷ 9 kitna hai?

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

    Jawab: (b) 6

  2. Do ankon ke number aur uske ulte number ka jod hamesha kis se divisible hota hai?

    1. (a) 9
    2. (b) 10
    3. (c) 11
    4. (d) 13
    Jawab dekho

    Jawab: (c) 11

  3. 1, 4 aur 6 ko ek-ek baar lekar, do ankon aur ek ank ke number ka sabse bada guna hai:

    1. (a) 64 × 1
    2. (b) 61 × 4
    3. (c) 41 × 6
    4. (d) 14 × 6
    Jawab dekho

    Jawab: (c) 41 × 6

  4. 637637, 13 se divisible kyon hai?

    Jawab dekho

    Jawab: Kyonki 637637 = 637 × 1001, aur 1001 = 7 × 11 × 13.

  5. Dikhaaiye ki 123 + 231 + 312, 37 se divisible hai.

    Jawab dekho

    Jawab: Ank ghumaakar jodne par jod 111 × (1 + 2 + 3) = 666 aata hai, aur 666 = 3 × 37 × 6.

Students ke sawal

Number aur uske ulte number ka antar 9 se divisible kyon hota hai?

10a + b aur 10b + a likhne par antar 9a − 9b = 9 × (a − b) aata hai. Bhaagfal bas dono ankon ka antar hai.

Number aur uska ulta jodne par kya hota hai?

Jod (10a + b) + (10b + a) = 11a + 11b = 11 × (a + b) hai, isliye wo hamesha 11 se divisible hai, aur bhaagfal ankon ka jod hai, jaise 28 + 82 = 110 = 11 × 10.

Teen ankon se sabse bada guna kaise dhoondhein?

Sabse bade ank ko multiplier banaaiye aur baaki do ko ghatte kram mein rakhkar do ankon ka number banaaiye. 2, 3 aur 5 se ye 32 × 5 = 160 deta hai.

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