How to Do Long Division: Divide, Multiply, Subtract, Bring Down

The four-step cycle

Long division is one small loop repeated: divide, multiply, subtract, bring down. Each turn of the loop produces one digit of the answer, working left to right through the dividend. Because you only ever divide by a single fitting count at a time, the arithmetic stays small even for large numbers.

The trick is discipline: always do the four steps in the same order, and never bring down more than one digit per cycle. If the divisor does not fit into the current number, you write a 0 in the quotient and bring down another digit before trying again.

A worked example: 528 ÷ 4

Start with the first digit, 5. Divide: 4 fits into 5 once, so write 1. Multiply: 1 × 4 = 4. Subtract: 5 − 4 = 1. Bring down the 2 to make 12. Divide: 4 fits into 12 three times, write 3. Multiply: 3 × 4 = 12. Subtract: 12 − 12 = 0. Bring down the 8 to make 8.

Now the last cycle: divide 8 by 4 to get 2, multiply 2 × 4 = 8, subtract 8 − 8 = 0. No digits remain and the difference is 0, so 528 ÷ 4 = 132 exactly. Reading the quotient digits top to bottom — 1, 3, 2 — gives 132.

Reading the remainder

Change the problem slightly to 529 ÷ 4. Everything runs the same until the final subtraction: dividing 9 by 4 gives 2, and 2 × 4 = 8, so 9 − 8 = 1. There are no more digits to bring down, so the leftover 1 is the remainder. The answer is 132 remainder 1.

You can express that remainder as a fraction over the divisor: 529 ÷ 4 = 132 and 1/4, or as a decimal 132.25 by adding a decimal point and continuing to bring down zeros. Which form you use depends on whether you need a whole-number remainder or a precise decimal value.

Frequently asked questions

What do the four steps stand for?

Divide, Multiply, Subtract, Bring down. You repeat this cycle once for each digit of the dividend until every digit has been used.

What if the divisor does not fit into the first digit?

Take the first two digits together instead. For 528 ÷ 6, since 6 does not fit into 5, start with 52 (6 fits 8 times) and continue from there.

When do I write a zero in the quotient?

Whenever the divisor does not fit into the current number after bringing a digit down. Write a 0 above that digit, then bring down the next one and continue.

How can I check the answer?

Multiply the quotient by the divisor and add the remainder — you should get the original dividend. For 132 × 4 + 1 = 529, which confirms 529 ÷ 4 = 132 remainder 1.