Long division is the division algorithm applied one place-value column at a time, from the biggest place down. Because a number like 728 means 7 hundreds+2 tens+8 ones, we divide the hundreds first, carry the leftover into the tens, and so on.
Imagine sharing 728 marbles into 6 boxes. First deal out the big bags of 100: you can put 1 hundred in each box (6 hundreds used), 1 hundred left. Break that leftover hundred into tens, mix with the tens you had, deal those out, then do the same with the single marbles. Whatever marbles you can't deal evenly are the remainder. The number each box gets is the quotient, the pile you started with is the dividend, and the number of boxes is the divisor.
Division ka matlab simple hai: ek badi cheez ko barabar groups mein baantna aur dekhna ki kitna bacha. Jaise 728 marbles ko 6 boxes mein daalna. Yaha 728 hai dividend (jise baant rahe ho), 6 hai divisor (kitne groups), har box mein jitne jaate hain wo quotient, aur jo bach jaata hai wo remainder. Ek golden rule yaad rakho: remainder hamesha divisor se chhota hona chahiye — agar barabar ya bada ho gaya, matlab ek aur group ban sakta tha, quotient galat hai.
Long division bas ek organised tareeka hai place-value ke hisaab se — pehle hundreds, phir tens, phir ones. Har digit pe wahi 4 steps chalao: Divide, Multiply, Subtract, Bring down (yaad rakho "Does McDonald's Sell Burgers"). Jab ek digit neeche laao aur number abhi bhi divisor se chhota ho, to quotient mein 0 likhna mat bhoolna — ye sabse common galti hai jaise 308÷4=77 mein pehle 0 ka dhyaan.
Sabse important habit: answer ko verify karo master formula se — Dividend = Divisor × Quotient + Remainder. 6×121+2=728, bilkul sahi. Aur agar remainder 0 aaye, iska matlab divisor number ko poori tarah divide karta hai (exactly divisible). Exam mein pehle estimate karo (forecast), jaise 623÷8 ka answer 70s mein hoga — isse chhoti-chhoti calculation mistakes turant pakad mein aa jaati hain. Ye chapter aage fractions, HCF-LCM aur remainders (modular arithmetic) ki neev hai.
