Long Division Calculator

About Long Division Calculator

See long division worked out step by step, exactly as you would write it by hand. Enter a dividend and divisor to see the quotient, remainder, and every bring-down step laid out clearly. Options to continue dividing for decimals and to see the result as a simplified fraction.

How Long Division Works

Long division follows a repeating four-step cycle: Divide, Multiply, Subtract, Bring Down. Here is the process for each digit of the quotient:

1. Divide: How many times does the divisor go into the current partial dividend?
2. Multiply: Multiply the quotient digit by the divisor
3. Subtract: Subtract the product from the partial dividend
4. Bring down: Bring down the next digit of the dividend

Worked example: 847 ÷ 3

Step	Action	Working
1	3 into 8	8 ÷ 3 = 2 remainder 2. Write 2 above.
2	Multiply and subtract	2 × 3 = 6. 8 - 6 = 2.
3	Bring down 4	New partial dividend: 24
4	3 into 24	24 ÷ 3 = 8 remainder 0. Write 8 above.
5	Multiply and subtract	8 × 3 = 24. 24 - 24 = 0.
6	Bring down 7	New partial dividend: 7
7	3 into 7	7 ÷ 3 = 2 remainder 1. Write 2 above.
8	Final	2 × 3 = 6. 7 - 6 = 1. Remainder is 1.

Result: 847 ÷ 3 = 282 remainder 1 (or 282.333... in decimal)

Verify: 282 × 3 + 1 = 846 + 1 = 847 ✓

Continuing to Decimals

When there is a remainder, you can continue dividing by adding a decimal point and bringing down zeros. The calculator supports up to 20 decimal places.

Worked example: 7 ÷ 4

1. 4 into 7 = 1 remainder 3
2. Add decimal point, bring down 0: 30
3. 4 into 30 = 7 remainder 2
4. Bring down 0: 20
5. 4 into 20 = 5 remainder 0
6. Result: 1.75 (terminates)

Some divisions never terminate. 1 ÷ 3 = 0.333... (repeating). 1 ÷ 7 = 0.142857142857... (repeating with a 6-digit cycle).

Division Results as Fractions

Every division can be expressed as a fraction: dividend/divisor. The calculator simplifies this by dividing both by their GCF:

Division	Fraction	GCF	Simplified	Decimal
15 ÷ 6	15/6	3	5/2	2.5
24 ÷ 9	24/9	3	8/3	2.666...
100 ÷ 8	100/8	4	25/2	12.5
45 ÷ 12	45/12	3	15/4	3.75

Verifying Your Answer

Always check division with this formula:

Dividend = Quotient × Divisor + Remainder

Division	Quotient	Remainder	Check
153 ÷ 7	21	6	21 × 7 + 6 = 147 + 6 = 153 ✓
500 ÷ 13	38	6	38 × 13 + 6 = 494 + 6 = 500 ✓
1234 ÷ 17	72	10	72 × 17 + 10 = 1224 + 10 = 1234 ✓

Repeating and Terminating Decimals

A division terminates (ends) when the remainder eventually reaches zero. It repeats when the same remainder appears a second time, creating a cycle.

Division	Result	Type	Why
1 ÷ 4	0.25	Terminating	Denominator factors are only 2s
1 ÷ 8	0.125	Terminating	Denominator factors are only 2s
1 ÷ 3	0.333...	Repeating (1 digit)	Denominator has factor of 3
1 ÷ 7	0.142857...	Repeating (6 digits)	Denominator has factor of 7
1 ÷ 6	0.1666...	Mixed	Denominator has factors 2 and 3

A fraction in lowest terms terminates if and only if the denominator has no prime factors other than 2 and 5.

Common Division Facts

Quick divisibility rules to check before starting long division:

Divisor	Rule	Example
2	Last digit is even	346 is divisible by 2
3	Sum of digits divisible by 3	123: 1+2+3 = 6, so yes
4	Last two digits divisible by 4	732: 32 ÷ 4 = 8, so yes
5	Ends in 0 or 5	235 is divisible by 5
6	Divisible by both 2 and 3	132: even and 1+3+2 = 6
9	Sum of digits divisible by 9	729: 7+2+9 = 18, so yes
10	Ends in 0	340 is divisible by 10

For remainder-focused calculations in programming contexts, the modulo calculator handles the mod operation with negative number support. For simplifying the fraction results, the fraction calculator does full arithmetic.

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