How to do long division
Long division breaks a big division into small steps you repeat: divide, multiply, subtract, bring down. This guide works through an example with a remainder and one with a decimal answer, and shows how to check yourself.
The short version
- Divide: how many times does the divisor fit into the current number?
- Multiply: multiply that digit by the divisor and write the result underneath.
- Subtract: the difference must be smaller than the divisor.
- Bring down the next digit of the dividend and repeat until there are no digits left.
Skip the arithmetic. The free Long Division Calculator does this for you, shows the formula and the working with your own numbers, and runs in your browser - nothing you type is uploaded. Also useful: Fraction Calculator, GCF & LCM Calculator.
Example: 1234 ÷ 5
Checking your answer
Multiply the quotient by the divisor and add the remainder. You should get the dividend back: 246 × 5 + 4 = 1230 + 4 = 1234. The remainder must always be smaller than the divisor; if it is not, the last digit of the quotient was too small.
Continuing into decimals
Instead of stopping with a remainder, put a decimal point after the quotient and keep bringing down zeros. 100 ÷ 7:
When a remainder repeats a value you have already seen, the digits from that point repeat forever. Here the remainder 2 returns after six steps, so 285714 repeats and the answer is written 14.(285714). Some divisions terminate: 1 ÷ 8 = 0.125, because the remainders reach 0.
Dividing by a decimal
Multiply both numbers by the same power of 10 so the divisor becomes a whole number. 4.5 ÷ 0.3 becomes 45 ÷ 3 = 15. The answer does not change because you scaled both numbers equally.
Mistakes to avoid
- Forgetting to bring down a digit, especially a zero. 4,012 ÷ 4 = 1,003 needs a 0 in the quotient each time 4 does not go into the new number.
- Misaligning the quotient digits above the dividend.
- Subtracting wrongly across a borrow. Check by multiplying back.