Long division has four names you must know before the first step:
Dividend — the number being divided (goes inside the bracket). Example: in 125 ÷ 4, the dividend is 125.
Divisor — the number you are dividing by (goes outside the bracket). In 125 ÷ 4, the divisor is 4.
Quotient — the answer, written above the bracket.
Remainder — what is left over when the divisor does not divide evenly. Written as "R" followed by the leftover number.
The Lesson: The Four-Step Loop
Long division is one algorithm repeated over and over until every digit of the dividend has been processed. The four steps are easy to remember with the mnemonic Does McDonald's Sell Burgers? — Divide, Multiply, Subtract, Bring down.
Divide. Look at the first digit (or first two digits) of the dividend. Ask: how many whole times does the divisor fit into those digits? Write that whole number above the bracket, directly over the digit(s) you used.
Multiply. Multiply the quotient digit you just wrote by the divisor. Write the product directly below the digits you divided in Step 1.
Subtract. Subtract the product (Step 2) from the digits above it. Write the difference on the next line. This difference must always be less than the divisor — if it is not, your Step 1 quotient digit was too small.
Bring Down. Write the next digit of the dividend beside the difference you just calculated. This new number becomes your working number for the next pass through the loop. If there are no more digits to bring down, you have reached the remainder.
Worked Example 1 — 96 ÷ 4
Problem: 96 ÷ 4
Step 1 — Divide: 4 goes into 9 exactly 2 times (2 × 4 = 8).
Write 2 above the 9.
Step 2 — Multiply: 2 × 4 = 8. Write 8 below the 9.
Step 3 — Subtract: 9 − 8 = 1. Write 1 below the line.
Step 4 — Bring down: Bring the 6 down beside the 1, making 16.
--- Repeat the loop ---
Step 1 — Divide: 4 goes into 16 exactly 4 times.
Write 4 above the 6.
Step 2 — Multiply: 4 × 4 = 16. Write 16 below 16.
Step 3 — Subtract: 16 − 16 = 0. No remainder.
Step 4 — No more digits to bring down.
Result: 96 ÷ 4 = 24 ✓
Check: 24 × 4 = 96 ✓
Worked Example 2 — 137 ÷ 5 (with a remainder)
Problem: 137 ÷ 5
Dividend = 137 Divisor = 5
Pass 1:
Divide: 5 goes into 1 zero times. Bring 3 alongside → work with 13.
5 goes into 13 twice (2 × 5 = 10). Write 2 above the 3.
Multiply: 2 × 5 = 10. Write under 13.
Subtract: 13 − 10 = 3.
Bring down: Bring 7 → working number is 37.
Pass 2:
Divide: 5 goes into 37 seven times (7 × 5 = 35). Write 7 above the 7.
Multiply: 7 × 5 = 35.
Subtract: 37 − 35 = 2.
No more digits.
Result: 137 ÷ 5 = 27 R2
Or as a mixed number: 27 and 2/5
Check: 27 × 5 + 2 = 135 + 2 = 137 ✓
Forgetting to write a zero in the quotient. When the divisor is larger than the current digit, you must write 0 in the quotient for that position. Skipping it shifts every subsequent digit and ruins your answer.
Choosing a quotient digit that is too large. After multiplying, if your product is bigger than the working number, your quotient digit was too large. Go down by one and try again.
Not checking with multiplication. Always verify: (quotient × divisor) + remainder = dividend. This one check catches the vast majority of errors.
Misaligning columns. In long division, alignment is everything. Each quotient digit must sit directly above the digit that was last brought down. Use graph paper if you keep losing your place.
Stopping too early. Keep going until you have brought down every digit of the dividend. A common error is stopping after the first pass and writing an incomplete quotient.
Free MIT math resources covering arithmetic through advanced topics.
Frequently Asked Questions
What does the division symbol mean?
The division symbol (÷) means "split into equal groups." In long division notation, the number inside the bracket is the dividend and the number outside is the divisor.
What do I do when the divisor is larger than the digit?
Write 0 above that position in the quotient and bring down the next digit to form a two-digit working number.
What is a remainder in division?
A remainder is the amount left over after dividing as evenly as possible. For example, 17 ÷ 5 = 3 remainder 2, because 5 × 3 = 15 and 17 − 15 = 2.
How do I check my long division answer?
Multiply your quotient by the divisor, then add the remainder. The result should equal the original dividend. If 125 ÷ 4 = 31 R1, check with 31 × 4 + 1 = 125. ✓
Can I use long division for decimals?
Yes. Once you reach the ones place and still have a remainder, place a decimal point in the quotient and append a zero to the remainder to continue dividing.