Mathematics · Basics
Long Division Calculator — Steps, Remainder & Repeating Decimals
Divide one number by another the way it's taught at school: each step of bring down, divide, multiply and subtract is shown. Get the quotient with remainder, the mixed number, and the exact decimal answer with any repeating block identified, like 1 ÷ 7 = 0.(142857).
Your inputs
Quick start — try a typical case
Your result Live
Quotient
341 remainder 2
7,845 ÷ 23 = 341.(0869565217391304347826)
- Decimal
- 341.(0869565217391304347826) — the digits in brackets repeat forever
- Mixed Number
- 341 2/23
- Check
- 23 × 341 + 2 = 7845
Long division
7845 ÷ 23
1: Step 1 · Bring down 8
78 ÷ 23 = 3; 3 × 23 = 69; 78 − 69
Expression becomes 9
2: Step 2 · Bring down 4
94 ÷ 23 = 4; 4 × 23 = 92; 94 − 92
Expression becomes 2
3: Step 3 · Bring down 5
25 ÷ 23 = 1; 1 × 23 = 23; 25 − 23
Expression becomes 2
Quotient 341, remainder 2
How this is calculated
dividend = divisor × quotient + remainder, 0 ≤ remainder < divisor
- Repeating decimal
- When a remainder comes round again, the digits from that point repeat
Work from the left: bring down the next digit, see how many times the divisor goes in, write that digit of the answer, multiply back and subtract. What's left at the end is the remainder. Carrying on past the decimal point gives the decimal answer; as soon as a remainder repeats, the digits after it repeat too.
Assumptions & sources
- Decimals are cleared first by moving the point in both numbers by the same number of places — the quotient is unchanged, but the remainder is in those scaled units.
Calculator ID MATH-LONGDIV-001 · version 1.0.0
Common questions
What is 7845 ÷ 23?
341 remainder 2 — 341.0869565217391304347826… with '0869565217391304347826' repeating.
Why does 1 ÷ 7 repeat?
There are only 6 possible non-zero remainders when dividing by 7, so they must cycle — giving the repeating block 142857.
How do I divide by a decimal?
Move the decimal point in both numbers until the divisor is whole: 4.5 ÷ 0.15 = 450 ÷ 15 = 30.