Long division looks intimidating until you realize it is the same four tiny steps repeated over and over: divide, multiply, subtract, bring down. Once you can do one cycle, you can divide numbers of any size. This guide walks through the method with fully worked examples, then shows you how to check your answer and avoid the classic mistakes.
The vocabulary: dividend, divisor, quotient, remainder
Four words do all the work in division:
Dividend — the number being divided (the big one inside the bracket).
Divisor — the number you divide by (outside the bracket).
Quotient — the answer: how many whole times the divisor fits.
Remainder — what is left over when it does not fit evenly.
In 47 ÷ 5: 47 is the dividend, 5 is the divisor, 9 is the quotient, 2 is the remainder.
The 4-step cycle
Write the problem in the standard layout, then repeat:
Divide: How many times does the divisor go into the current working number? Write that digit in the quotient.
Multiply: Multiply the divisor by the digit you just wrote.
Subtract: Subtract the product from the working number.
Bring down: Bring down the next digit of the dividend next to the remainder. This is your new working number — go back to step 1.
A handy mnemonic students use: "Divide, Multiply, Subtract, Bring down" — or "Dad, Mother, Sister, Brother."
Worked example 1: 847 ÷ 7
121
┌─────
7 │847
7
─
14
14
──
07
7
──
0
Step 1: 7 goes into 8 one time. Write 1. 1 × 7 = 7. 8 − 7 = 1. Bring down the 4 → working number 14.
Step 2: 7 goes into 14 two times. Write 2. 2 × 7 = 14. 14 − 14 = 0. Bring down the 7 → working number 7.
Step 3: 7 goes into 7 one time. Write 1. 1 × 7 = 7. 7 − 7 = 0. No digits left.
Answer: 847 ÷ 7 = 121 exactly.
Worked example 2: with a remainder — 953 ÷ 6
6 into 9 → 1 (1 × 6 = 6; 9 − 6 = 3). Bring down 5 → 35.
6 into 35 → 5 (5 × 6 = 30; 35 − 30 = 5). Bring down 3 → 53.
6 into 53 → 8 (8 × 6 = 48; 53 − 48 = 5). No digits left.
Answer: 953 ÷ 6 = 158 remainder 5.
What about zeros in the quotient?
Sometimes the divisor does not fit into the working number at all — for example, the middle step of 1,205 ÷ 5. When that happens, write 0 in the quotient, skip the multiply/subtract (or write 0), and bring down the next digit. Beginners often forget this zero, which shifts every later digit left and ruins the answer. If your quotient looks suspiciously short, a missing zero is the prime suspect.
How to check your answer
Every division can be verified with one formula:
Divisor × Quotient + Remainder = Dividend
Check example 2: 6 × 158 + 5 = 948 + 5 = 953 ✓. If the check fails, the error is usually in one subtraction step — rework just the subtractions first.
Common mistakes (and how to avoid them)
Mistake
Fix
Forgetting the 0 in the quotient
Every bring-down gets a quotient digit, even if it is 0
Subtraction errors
Double-check each subtraction before bringing down
Misaligned digits
Use graph paper — one digit per square
Bringing down two digits at once
One digit per cycle, no exceptions
Remainder larger than divisor
Impossible — it means the quotient digit was too small
What is the easiest way to remember long division steps?
Use the mnemonic "Divide, Multiply, Subtract, Bring down" (or "Dad, Mother, Sister, Brother"). Say it before each cycle until it becomes automatic.
When do you put a zero in the quotient?
Whenever the divisor doesn't fit into the current working number — write 0 in the quotient and bring down the next digit. Skipping this zero is the #1 beginner mistake.
Can the remainder be bigger than the divisor?
Never. If your remainder is as big as (or bigger than) the divisor, your quotient digit was too small — go back one step and try the next higher digit.
How do you do long division with decimals?
For a decimal dividend, bring the decimal point straight up into the quotient. For a decimal divisor, multiply both numbers by 10 (repeatedly) until the divisor is whole, then divide normally.
Why is it called "long" division?
To distinguish it from "short" division, where you do the divide-multiply-subtract steps mentally and only write the quotient. Long division writes out every step — which is exactly what makes it reliable for big numbers.