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Long Division Calculator
Divide positive whole numbers and see the quotient, remainder, and every long-division step in the bracket students draw.
The number being divided, up to 8 digits
The number you divide by, up to 4 digits
125 ÷ 4 = 31 R1
Formula
dividend = divisor × quotient + remainder
With your numbers
125 = 4 × 31 + 1
Quotient
Remainder
125 ÷ 4 = 31 R1
Long division
Highlighted digits were brought down from the dividend.
Steps
- 1 is smaller than 4, so take digits until the number is at least the divisor. 12 ÷ 4 = 3. Write 3 in the tens place. 4 × 3 = 12. Subtract 12 − 12 = 0. Bring down 5. The bracket shows 05, which equals 5.
- 05 ÷ 4 = 1. Write 1 in the ones place. 4 × 1 = 4. Subtract 05 − 4 = 1. No digits are left to bring down. The remainder is 1.
This long division calculator is for students practicing the standard algorithm with positive whole numbers. Enter a dividend of up to 8 digits and a divisor of up to 4 digits, and the page draws the bracket, places the quotient above the dividend, and shows each multiply, subtract, and bring-down step in its place. The quotient and the remainder appear above that work, along with the check dividend = divisor × quotient + remainder filled in with your numbers. A divisor of 0 is explained as undefined, and the boxes stay with positive whole numbers so a decimal or a negative does not enter the tableau.
How the steps move across the bracket
The divisor sits outside the bracket and the dividend sits under the quotient. Starting at the left, digits are taken until the number is at least as large as the divisor. That number is divided, the quotient digit is written above the matching place, the divisor is multiplied by that digit, and the product is subtracted. The next dividend digit is brought down beside the difference, and the same moves repeat until every digit has been used.
A quotient digit lines up with the place it belongs to, so in 560 divided by 8 the 7 is in the tens place and the 0 is in the ones place. That 0 appears because 8 does not fit into the 0 that was brought down. The last difference is the remainder, and it is smaller than the divisor. When the remainder is 0, the dividend divides evenly, as with 847 divided by 7, which is 121.
The equation that checks the answer
Every finished problem follows dividend = divisor × quotient + remainder. For 125 divided by 4 the bracket gives quotient 31 and remainder 1, and 4 × 31 + 1 equals 125. For 100 divided by 3 the quotient is 33 and the remainder is 1, and 3 × 33 + 1 equals 100. Compare that line with a problem worked on paper before copying the quotient into an answer blank.
Frequently Asked Questions
What do the quotient and the remainder mean?
The quotient is the whole-number result written above the bracket. The remainder is what is left after the last subtraction, and it is smaller than the divisor. In 125 divided by 4 the quotient is 31 and the remainder is 1.
How do you check a long-division answer?
Multiply the divisor by the quotient and add the remainder. The result should be the dividend. The calculator writes that check as dividend = divisor × quotient + remainder, then fills in your numbers.
Why is division by zero undefined?
Division by zero is undefined. A divisor of 0 does not name a group you can make, so there is no quotient and no remainder that satisfy the check equation. The page says so in words.
Can this calculator use decimals or negative numbers?
The tableau is for positive whole numbers. Type digits only, up to 8 in the dividend and 4 in the divisor. A decimal point or a minus sign has to be cleared before the steps can be drawn.
Why does 560 divided by 8 have a 0 in the answer?
8 goes into 56 seven times, which is the tens digit. Bringing down the last 0 makes 0, and 8 fits into 0 zero times, so the ones digit is 0. The quotient is 70 and the remainder is 0.