Long division — step by step
Long division is a four-step cycle. Once you have the cycle in your fingers, any dividend with any number of digits is just the same routine repeated.
The four repeating steps
- Divide — how many times does the divisor go into the current digit (or group of digits) of the dividend?
- Multiply — multiply the divisor by the quotient digit you just wrote.
- Subtract — subtract that product from the current portion of the dividend.
- Bring down — bring down the next digit of the dividend and start the cycle again.
When there are no more digits to bring down, the last difference is the remainder (or 0 if the division was exact).
Worked example: 936 ÷ 4
1. Look at the first digit: 9.
How many times does 4 fit into 9? 2 times (4 × 2 = 8).
Write 2 as the first quotient digit. Subtract 9 − 8 = 1.
2. Bring down the next digit: 3. You now have 13.
How many times does 4 fit into 13? 3 times (4 × 3 = 12).
Write 3. Subtract 13 − 12 = 1.
3. Bring down the next digit: 6. You now have 16.
How many times does 4 fit into 16? 4 times (4 × 4 = 16).
Write 4. Subtract 16 − 16 = 0.
Result: 936 ÷ 4 = 234, no remainder.
Column layout
In school we write long division like this:
936 ÷ 4 = 234
8
--
13
12
--
16
16
--
0You write the quotient digits as you find them, one at a time, to the right of the equals sign. You don't have to plan them out in advance.
When the divisor is too big for the first digit
Sometimes the first digit of the dividend is smaller than the divisor.
235 ÷ 4 = ?
4 doesn't fit into 2 at all. In that case, take the first two digits together: 23.
1. 4 fits into 23 5 times (4 × 5 = 20). Write 5. Subtract: 23 − 20 = 3.
2. Bring down 5: now you have 35.
3. 4 fits into 35 8 times (4 × 8 = 32). Write 8. Subtract: 35 − 32 = 3.
Result: 235 ÷ 4 = 58 remainder 3.
The quotient has one fewer digit than the dividend, because the divisor didn't fit into the first digit.