Long Division Calculator with Remainders (Step by Step)

Enter the dividend (the number being divided) and the divisor. You get the long division, a step-by-step explanation for each place, the quotient and remainder, a mixed number and a decimal, all at once.

Dividend

Divisor

Method

Enter numbers greater than 0, up to 14 digits each. Decimals are fine too (they are multiplied by 10, 100 and so on to make a whole-number division). "Divide into decimals" keeps going until the division comes out even (up to 10 decimal places).

Result

Enter the dividend and the divisor in the fields on the left and press "Calculate". The long division and the result will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formulas and figure
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter the dividend and the divisor, and the long division appears on the spot, laid out just as you would write it on paper (the quotient and the remainder are easy to see)
Each step is explained in order, place by place: what was divided, multiplied, subtracted and brought down
Choose between "Find the remainder" and "Divide into decimals" (in decimal mode, the long division continues into the decimal places)
Decimal division such as $12.5 \div 0.5$ works too. The steps show how multiplying both numbers by 10 or 100 turns it into a whole-number division
The answer is also shown as a mixed number (in simplest form) and as a decimal. A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

Only numbers greater than 0 (positive numbers) can be used. The dividend and the divisor can each have up to 14 digits, and dividing into decimals goes up to 10 decimal places.

What is this calculation used for?

Sharing equally every day (snacks, worksheets, supplies)

Share 100 candies equally among 7 kids: 100 ÷ 7 = 14 R2, so each kid gets 14 and 2 are left over.
Handing out worksheets in class, splitting supplies between groups, sharing a treat with the family: getting "how many each, and how many left" in one step is where division with remainders shows up most often.

How the calendar works (1 year = 52 weeks and 1 day)

Divide the 365 days of a year by the 7 days of a week: 365 ÷ 7 = 52 R1. A year is "52 weeks and 1 day", so the same date next year falls one day of the week later (in a leap year, 366 ÷ 7 = 52 R2, so it moves two days).
To find "what day of the week is it in N days?", you only need the remainder after dividing by 7.

Planning boxes and shipments (logistics and manufacturing)

Packing 250 items into boxes of 8: 250 ÷ 8 = 31 R2, so 31 boxes are full and 2 items are left. To ship everything, you need 32 boxes, including one for the last 2 items.
The idea "quotient, plus one more if there is a remainder" is used every day in logistics and production planning, for example to find how many trucks, or how many buses for a group of people.

Splitting a bill that does not divide evenly

Split a $100 bill among 3 people. In cents, 10,000 ÷ 3 = 3,333 R1, so each person pays $33.33 and 1 cent is left over.
Money cannot be split into less than 1 cent, so splitting bills, making change and saving up are best thought of as "quotient and remainder". Someone pays 1 cent more, or the organizer covers the extra: the remainder tells you what needs to be settled.

A basic operation in programming (clocks, even or odd, sharing out data)

"What time is it 100 hours from now?" 100 ÷ 24 = 4 R4, so it is 4 days and 4 hours later. Calculations that go around and start over, like a clock, are usually written with the remainder (the mod or % operator) in programming.
Checking whether a number is even (remainder 0 when divided by 2) or odd (remainder 1), and spreading data evenly across machines, are also remainder calculations running inside computers all the time.

Formulas and figure

One step of long division (divide, multiply, subtract, bring down)

Long division example

Standard notation (the usual math form)

$q_i$ $=$ $\lfloor$ $s_i$ $\div$ $b$ $\rfloor$

In words (symbols replaced with words)

③ $q_i$: quotient digit for this place $=$ $\lfloor$ ① $s_i$: number you are working with $\div$ ② $b$: divisor $\rfloor$

The formula in words

① Take the $s_i$: number you are working with (what was left from the step before, with the next digit brought down)

② and see how many times the $b$: divisor goes into it (divide, then drop the decimal part with the floor symbol $\lfloor\ \rfloor$)

③ and write that number above as the $q_i$: quotient digit for this place (divide). Then write "divisor × that digit" below and subtract it (multiply, subtract), and bring down the next digit (bring down). Repeat until you reach the ones place, or the decimal places when you divide into decimals

Quick example

The first step of 100 ÷ 7 (the tens place, the top step in the figure above) is

digit for the tens place (1) $=$ $\lfloor$ number you are working with (10) $\div$ divisor (7) $\rfloor$

$\lfloor 10 \div 7 \rfloor = 1$

$7 \times 1 = 7$

$10 - 7 = 3$

Key idea

Long division breaks one big division into a series of small divisions you can do with your multiplication facts. Every step does the same four things: divide, multiply, subtract, bring down. In the figure above, 100 ÷ 7 solves 10 ÷ 7 in the tens place and 30 ÷ 7 in the ones place (the leading 1 is smaller than 7, so no quotient digit goes above the hundreds place). When the divisor has 2 or more digits, round it to estimate the quotient digit. For 73 ÷ 24, think of 24 as about 20, so the digit is about 3. Multiply to check, and if the product is too big, try 1 less. If a quotient digit is 0, still write the 0 and move on. For example, 6120 ÷ 6 = 1020. Forgetting the 0 in the middle shifts the digits and gives a completely different answer. As in US schools, the figure writes a minus sign in front of each number you subtract, and it writes the remainder after the quotient with an R (14 R2). If there is a remainder, you can also keep going into decimals: put a decimal point in the quotient, bring down a 0 and repeat the same four steps. Choose "Divide into decimals" in the calculator to see that long division continue into the decimal places.

Division and how to check it (dividend, divisor, quotient and remainder)

Standard notation (the usual math form)

$a$ $=$ $b$ $\times$ $q$ $+$ $r$

In words (symbols replaced with words)

④ $a$: dividend $=$ ① $b$: divisor $\times$ ② $q$: quotient $+$ ③ $r$: remainder

The formula in words

① Multiply the $b$: divisor

② by the $q$: quotient

③ and add the $r$: remainder

④ to get back the $a$: dividend (this is how you check the answer)

Quick example

Checking 100 ÷ 7 = 14 R2:

dividend (100) $=$ divisor (7) $\times$ quotient (14) $+$ remainder (2)

$7 \times 14 = 98$

$98 + 2 = 100$

Key idea

The remainder is always at least 0 and smaller than the divisor ($0 \le r < b$). If the remainder is equal to or larger than the divisor, the quotient can go up by 1. For example, 100 ÷ 7 = 13 R9 is wrong: 7 still fits into 9 once more, so the correct answer is 14 R2. Putting your answer into this formula and seeing whether you get back the dividend is the surest way to check a division.

Finding the quotient (how many times the divisor goes in)

Standard notation (the usual math form)

$q$ $=$ $\lfloor$ $a$ $\div$ $b$ $\rfloor$

In words (symbols replaced with words)

④ $q$: quotient $=$ $\lfloor$ ① $a$: dividend $\div$ ② $b$: divisor ③ $\rfloor$

The formula in words

① Divide the $a$: dividend

② by the $b$: divisor

③ drop the decimal part of the answer (the part that did not divide evenly) with the symbol $\lfloor\ \rfloor$

④ and you get the $q$: quotient

Quick example

The quotient of 100 ÷ 7 is

quotient (14) $=$ $\lfloor$ dividend (100) $\div$ divisor (7) $\rfloor$

$100 \div 7 = 14.285\cdots$

$\lfloor 14.285\cdots \rfloor = 14$

Key idea

$\lfloor\ \rfloor$ is the floor function: it drops the decimal part and leaves a whole number. Some textbooks call it the greatest integer function and write it as $[x]$. In long division, you find the quotient one digit at a time from the left by asking "how many times does the divisor go in?". The result is exactly the same as dividing and then dropping the decimal part.

Finding the remainder (what is left after subtracting)

Standard notation (the usual math form)

$r$ $=$ $a$ $-$ $b$ $\times$ $q$

In words (symbols replaced with words)

④ $r$: remainder $=$ ① $a$: dividend $-$ ② $b$: divisor $\times$ ③ $q$: quotient

The formula in words

① From the $a$: dividend

② subtract the $b$: divisor

③ times the $q$: quotient (the part that was shared out evenly)

④ and you get the $r$: remainder

Quick example

The remainder of 100 ÷ 7 (quotient 14) is

remainder (2) $=$ dividend (100) $-$ divisor (7) $\times$ quotient (14)

$7 \times 14 = 98$

$100 - 98 = 2$

Key idea

The remainder is what is left after you take away the part that was shared out evenly (divisor × quotient) from the dividend. In programming, this is the "mod" or "%" operator, written as 100 mod 7 = 2. It is used all the time in computing, for example to work out days of the week or to tell even numbers from odd ones.

Writing the answer as a mixed number or a decimal

Standard notation (the usual math form)

$a$ $\div$ $b$ $=$ $q$ $+$ $r$ $\div$ $b$

In words (symbols replaced with words)

① $a$: dividend $\div$ ② $b$: divisor $=$ ③ $q$: quotient $+$ ④ $r$: remainder $\div$ ⑤ $b$: divisor

The formula in words

① Dividing the $a$: dividend

② by the $b$: divisor gives

③ the $q$: quotient

④ plus the $r$: remainder

⑤ divided by the $b$: divisor (together, a mixed number)

Quick example

100 ÷ 7 as a mixed number is

dividend (100) $\div$ divisor (7) $=$ quotient (14) $+$ remainder (2) $\div$ divisor (7)

$\dfrac{100}{7} = 14 + \dfrac{2}{7} = 14\dfrac{2}{7}$

Key idea

Write the fraction part, remainder ÷ divisor, in simplest form. For example, 123456 ÷ 789 = 156 R372. Divide the numerator and the denominator of $\dfrac{372}{789}$ by their greatest common factor, 3, and you get $156\dfrac{124}{263}$. To get a decimal instead, do not stop at the remainder and keep dividing (100 ÷ 7 = 14.2857…). If it never comes out even, the answer is a repeating decimal, where the same group of digits repeats forever.

Long division just repeats "divide, multiply, subtract, bring down" from the leftmost place down to the ones place (or into the decimal places when you divide into decimals). You can always check the answer with "divisor × quotient + remainder = dividend". The quotient tells how many times the divisor goes in, and the remainder is what is left after subtracting.

Symbols and terms

Symbols

$a$	a	The dividend, the number being divided. (Example - the 100 in 100 ÷ 7)
$b$	b	The divisor, the number you divide by. It is the "how many groups" or "how many in each group" number. (Example - the 7 in 100 ÷ 7)
$q$	q	The quotient, the whole-number answer of the division. It tells how many times the divisor goes in. (Example - 14 for 100 ÷ 7)
$r$	r	The remainder, the part left over that cannot be shared out. It is always at least 0 and smaller than the divisor. (Example - 2 for 100 ÷ 7)
$s_i$	s sub i	The number you are working with in one step of long division. It is what was left from the subtraction in the step before, with the next digit brought down next to it. (Example - in the ones step of 100 ÷ 7, the 3 left over with the 0 brought down makes 30)
$q_i$	q sub i	The quotient digit for one place (one of 0 to 9). It is how many times the divisor goes into the number you are working with. Written in order from the left, these digits make the quotient.
$\lfloor\ \rfloor$	floor	The floor function. It drops the decimal part of the number inside and leaves a whole number. (Example - $\lfloor 14.28 \rfloor = 14$)
14 R2	fourteen R two	The usual way US schools write "quotient 14, remainder 2". R stands for remainder. The long division on this page writes it after the quotient in the same way.

Terms

dividend	The number being divided. The 100 in "100 ÷ 7". In long division it goes inside the division bracket.
divisor	The number you divide by. The 7 in "100 ÷ 7". In long division it goes to the left of the division bracket. You cannot divide by 0.
quotient	The answer of a division. In division with remainders, it is the whole-number part of the answer. In long division it is written above the division bracket.
remainder	The part left over that cannot be shared out. It is always at least 0 and smaller than the divisor. In programming it is found with the % (mod) operator.
long division	The written method for dividing large numbers on paper. You find the quotient one digit at a time from the left by repeating four steps - divide, multiply, subtract, bring down.
divide, multiply, subtract, bring down	The four steps of long division. Write the quotient digit above (divide), write divisor × that digit below (multiply), subtract (subtract), and copy the next digit down next to what is left (bring down). Repeat for each place.
annexing zeros	Writing zeros after the decimal point of the dividend so you can keep dividing into the decimal places instead of stopping at a remainder. (Example - 9 ÷ 4 is 2 R1, but writing 9 as 9.00 and continuing gives 2.25)
checking the answer	Making sure an answer is right with a different calculation. For division, check that "divisor × quotient + remainder" gives back the dividend.
mixed number	A whole number and a proper fraction written together, such as $14\dfrac{2}{7}$ (fourteen and two sevenths). It is one way to write the answer of a division with a remainder.
simplest form	A fraction whose numerator and denominator have no common factor other than 1. You get it by dividing both by their greatest common factor. (Example - $\dfrac{372}{789}$ → $\dfrac{124}{263}$)
divides evenly	When the remainder is 0. (Example - 1000 ÷ 25 = 40 divides evenly, but 100 ÷ 7 does not)
repeating decimal	A decimal in which the same group of digits repeats forever, which happens when a division never comes out even. (Example - 100 ÷ 7 = 14.285714285714… repeats "285714")

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Multiplication facts (Grade 3)	Knowing multiplication facts such as 7 × 8 = 56 quickly (they are the basis for finding each quotient digit)
What division is, and remainders (Grades 3–4)	Knowing that division finds "how many in each equal share" or "how many times a number fits" Knowing that the remainder is always smaller than the divisor
Long division (Grades 4–6)	Being able to follow the four steps - divide, multiply, subtract, bring down Being able to estimate each quotient digit by rounding a 2-digit divisor to the nearest ten Being able to check the answer with "divisor × quotient + remainder"
Fractions, mixed numbers and simplifying (Grades 4–5)	Being able to write the answer of a division with a remainder as a mixed number, the quotient next to $\dfrac{\text{remainder}}{\text{divisor}}$ Being able to simplify a fraction by dividing the numerator and the denominator by the same number
Decimals and dividing into decimals (Grades 5–6)	Knowing that multiplying a decimal by 10 or 100 moves the decimal point 1 or 2 places to the right (used to turn a decimal division into a whole-number division) Being able to keep dividing into the decimal places instead of stopping at a remainder, by putting a decimal point in the quotient and bringing down zeros (example - 9 ÷ 4 = 2.25)

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to find the quotient

Dividend a	100
Divisor b	7
Quotient q	=INT(B1/B2)

Table to find the remainder

Dividend a	100
Divisor b	7
Remainder r	=MOD(B1,B2)

Table to check the answer (divisor × quotient + remainder)

Divisor b	7
Quotient q	14
Remainder r	2
Dividend a (check)	=B1*B2+B3

Table to write the answer as a mixed number or a decimal

Dividend a	100
Divisor b	7
Quotient (whole-number part)	=INT(B1/B2)
Numerator of the fraction part (remainder)	=MOD(B1,B2)
As a decimal	=B1/B2

After pasting, B1 and B2 are your inputs and the formula cells are calculated automatically.
"INT" drops the decimal part (the quotient) and "MOD" finds the remainder. You can also get the quotient with "=QUOTIENT(B1,B2)".
The first table shows 14 in B3, the second table shows 2 in B3, and the fourth table shows about 14.2857 in the decimal row. Just replace B1 and B2 with your own numbers.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to find the quotient

Dividend a	100
Divisor b	7
Quotient q	=INT(B1/B2)

Table to find the remainder

Dividend a	100
Divisor b	7
Remainder r	=MOD(B1,B2)

Table to check the answer (divisor × quotient + remainder)

Divisor b	7
Quotient q	14
Remainder r	2
Dividend a (check)	=B1*B2+B3

Table to write the answer as a mixed number or a decimal

Dividend a	100
Divisor b	7
Quotient (whole-number part)	=INT(B1/B2)
Numerator of the fraction part (remainder)	=MOD(B1,B2)
As a decimal	=B1/B2

The same formulas as in Excel (INT, MOD and QUOTIENT) work as is. Copy the whole table, paste it into cell A1, and replace B1 and B2 with your own numbers.

How to calculate it in Python

dividend = 100  # the number being divided
divisor = 7     # the number you divide by

quotient, remainder = divmod(dividend, divisor)  # quotient and remainder at once

print(f"Quotient: {quotient}")
print(f"Remainder: {remainder}")
print(f"Check: {divisor} × {quotient} + {remainder} = {divisor * quotient + remainder}")
print(f"As a decimal: {dividend / divisor}")

Runs with the standard library only. divmod(a, b) returns the quotient and the remainder together. To get them separately, write "a // b" for the quotient (division that drops the decimal part) and "a % b" for the remainder. Change the first two numbers and run it.

How to write it in LaTeX and other math languages (copy and paste)

One step of long division (divide, multiply, subtract, bring down)

qᵢ = ⌊sᵢ ÷ b⌋

q_i = \left\lfloor s_i \div b \right\rfloor

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>q</mi><mi>i</mi></msub>
    <mo>=</mo>
    <mo>&#x230A;</mo>
    <msub><mi>s</mi><mi>i</mi></msub>
    <mo>&#xF7;</mo>
    <mi>b</mi>
    <mo>&#x230B;</mo>
  </mrow>
</math>

q_i = |__ s_i -: b __|

Floor[s/b]

q := floor(s/b);

q = floor(s/b);

q_i = ⌊s_i/b⌋

Division and how to check it (dividend, divisor, quotient and remainder)

a = b × q + r

a = b \times q + r

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>a</mi>
    <mo>=</mo>
    <mi>b</mi>
    <mo>&#xD7;</mo>
    <mi>q</mi>
    <mo>+</mo>
    <mi>r</mi>
  </mrow>
</math>

a = b xx q + r

b*q + r

a := b*q + r;

a = b*q + r;

a = b q + r

Finding the quotient (how many times the divisor goes in)

q = ⌊a ÷ b⌋

q = \left\lfloor \dfrac{a}{b} \right\rfloor

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>q</mi>
    <mo>=</mo>
    <mo>&#x230A;</mo>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>&#x230B;</mo>
  </mrow>
</math>

q = |__ a/b __|

Floor[a/b]

q := floor(a/b);

q = floor(a/b);

q = ⌊a/b⌋

Finding the remainder (what is left after subtracting)

r = a − b × q

r = a - b \times q

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>r</mi>
    <mo>=</mo>
    <mi>a</mi>
    <mo>&#x2212;</mo>
    <mi>b</mi>
    <mo>&#xD7;</mo>
    <mi>q</mi>
  </mrow>
</math>

r = a - b xx q

a - b*q

r := a - b*q;

r = a - b*q;

r = a − b q

Writing the answer as a mixed number or a decimal

a/b = q + r/b

\dfrac{a}{b} = q + \dfrac{r}{b}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>=</mo>
    <mi>q</mi>
    <mo>+</mo>
    <mfrac><mi>r</mi><mi>b</mi></mfrac>
  </mrow>
</math>

a/b = q + r/b

q + r/b

q + r/b;

x = q + r/b;

a/b = q + r/b

How to have ChatGPT do the calculation

You are a math calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

For the division 100 ÷ 7, find each of the following:
1. The quotient (whole-number answer) and the remainder
2. A check (divisor × quotient + remainder gives back the dividend)
3. The answer as a mixed number (with the fraction in simplest form)
4. The answer as a decimal

Show the formulas you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula

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\(a\)	a	The dividend, the number being divided. (Example - the 100 in 100 ÷ 7)
\(b\)	b	The divisor, the number you divide by. It is the "how many groups" or "how many in each group" number. (Example - the 7 in 100 ÷ 7)
\(q\)	q	The quotient, the whole-number answer of the division. It tells how many times the divisor goes in. (Example - 14 for 100 ÷ 7)
\(r\)	r	The remainder, the part left over that cannot be shared out. It is always at least 0 and smaller than the divisor. (Example - 2 for 100 ÷ 7)
\(s_i\)	s sub i	The number you are working with in one step of long division. It is what was left from the subtraction in the step before, with the next digit brought down next to it. (Example - in the ones step of 100 ÷ 7, the 3 left over with the 0 brought down makes 30)
\(q_i\)	q sub i	The quotient digit for one place (one of 0 to 9). It is how many times the divisor goes into the number you are working with. Written in order from the left, these digits make the quotient.
\(\lfloor\ \rfloor\)	floor	The floor function. It drops the decimal part of the number inside and leaves a whole number. (Example - \(\lfloor 14.28 \rfloor = 14\))
14 R2	fourteen R two	The usual way US schools write "quotient 14, remainder 2". R stands for remainder. The long division on this page writes it after the quotient in the same way.

Long Division Calculator with Remainders (Step by Step)

Table of Contents

What you can do on this page

What is this calculation used for?

Formulas and figure

Symbols and terms

Symbols

Terms

Good to know before you start

How to calculate it in Excel

How to calculate it in Google Sheets

How to calculate it in Python

How to write it in LaTeX and other math languages (copy and paste)

How to have ChatGPT do the calculation

How to Use

DataChef Features

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