Division of Large Numbers Notes
This Division of Large Numbers Calculator divides one large whole number by another using long division, and shows the working line by line. The digits of the dividend are brought down one at a time, and at each position the divisor is taken out as many whole times as it fits. Whatever is left at the end is the remainder. Following the same pattern every time keeps each digit of the quotient lined up with the digit it came from.
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
In this problem: We divide \(3672\) by \(18\). The quotient goes on top, and we work from left to right.
| 18 | 3 | 6 | 7 | 2 |
Step 2
Step 2 - Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
In this problem: We start with the first digit \(3\). Since \(18\) does not fit into \(3\), we include more digits from the left to make \(36\). Then we repeat: divide, multiply, subtract, bring down. The lettered steps below run through this cycle one turn at a time.
| 18 | 3 | 6 | 7 | 2 |
Step 2a
Step 2a - Check whether the divisor fits into the digits taken so far. If it does not, include the next digit from the dividend.
In this problem: We look at \(3\). \(18\) does not fit yet, so we include the next digit \(6\) to make \(36\).
| 18 | 3 | 6 | 7 | 2 |
Step 2b
Step 2b - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(36\). \(18\) fits \(2\) times. Multiply: \(18 \times 2 = 36\). Subtract: \(36 - 36 = 0\).
| 2 | ||||
| 18 | 3 | 6 | 7 | 2 |
| - | 3 | 6 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(6 - 6 = 0\) → write \(0\) under the ones column.
| 3 | 6 | |
| − | 3 | 6 |
| 0 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(3 - 3 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 3 | 6 | |
| − | 3 | 6 |
| 0 | ||
Final Answer
Step 2c
Step 2c - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(7\) next to the remainder \(0\). Now we have \(7\) to work with.
| 2 | ||||
| 18 | 3 | 6 | 7 | 2 |
| - | 3 | 6 | ||
| 0 | 7 |
Step 2d
Step 2d - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(7\). \(18\) does not fit, so we write \(0\) on top. The remainder stays \(7\).
| 2 | 0 | |||
| 18 | 3 | 6 | 7 | 2 |
| - | 3 | 6 | ||
| 0 | 7 | |||
| 7 |
Step 2e
Step 2e - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(2\) next to the remainder \(7\). Now we have \(72\) to work with.
| 2 | 0 | |||
| 18 | 3 | 6 | 7 | 2 |
| - | 3 | 6 | ||
| 0 | 7 | |||
| 7 | 2 |
Step 2f
Step 2f - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(72\). \(18\) fits \(4\) times. Multiply: \(18 \times 4 = 72\). Subtract: \(72 - 72 = 0\).
| 2 | 0 | 4 | ||
| 18 | 3 | 6 | 7 | 2 |
| - | 3 | 6 | ||
| 0 | 7 | |||
| 7 | 2 | |||
| - | 7 | 2 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(2 - 2 = 0\) → write \(0\) under the ones column.
| 7 | 2 | |
| − | 7 | 2 |
| 0 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(7 - 7 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 7 | 2 | |
| − | 7 | 2 |
| 0 | ||
Final Answer
Final Answer
See Example 2 Hide Example 2
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
In this problem: We divide \(812\) by \(4\). The quotient goes on top, and we work from left to right.
| 4 | 8 | 1 | 2 |
Step 2
Step 2 - Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
In this problem: We start with the first digit \(8\) because it is big enough to divide by \(4\). Then we repeat: divide, multiply, subtract, bring down. The lettered steps below run through this cycle one turn at a time.
| 4 | 8 | 1 | 2 |
Step 2a
Step 2a - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(8\). \(4\) fits \(2\) times. Multiply: \(4 \times 2 = 8\). Subtract: \(8 - 8 = 0\).
| 2 | |||
| 4 | 8 | 1 | 2 |
| - | 8 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(8 - 8 = 0\) → write \(0\) under the ones column.
| 8 | |
| − | 8 |
| 0 | |
Final Answer
Step 2b
Step 2b - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(1\) next to the remainder \(0\). Now we have \(1\) to work with.
| 2 | |||
| 4 | 8 | 1 | 2 |
| - | 8 | ||
| 0 | 1 |
Step 2c
Step 2c - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(1\). \(4\) does not fit, so we write \(0\) on top. The remainder stays \(1\).
| 2 | 0 | ||
| 4 | 8 | 1 | 2 |
| - | 8 | ||
| 0 | 1 | ||
| 1 |
Step 2d
Step 2d - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(2\) next to the remainder \(1\). Now we have \(12\) to work with.
| 2 | 0 | ||
| 4 | 8 | 1 | 2 |
| - | 8 | ||
| 0 | 1 | ||
| 1 | 2 |
Step 2e
Step 2e - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(12\). \(4\) fits \(3\) times. Multiply: \(4 \times 3 = 12\). Subtract: \(12 - 12 = 0\).
| 2 | 0 | 3 | |
| 4 | 8 | 1 | 2 |
| - | 8 | ||
| 0 | 1 | ||
| 1 | 2 | ||
| - | 1 | 2 | |
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(2 - 2 = 0\) → write \(0\) under the ones column.
| 1 | 2 | |
| − | 1 | 2 |
| 0 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(1 - 1 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 1 | 2 | |
| − | 1 | 2 |
| 0 | ||
Final Answer
Final Answer
See Example 3 Hide Example 3
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
In this problem: We divide \(2856\) by \(14\). The quotient goes on top, and we work from left to right.
| 14 | 2 | 8 | 5 | 6 |
Step 2
Step 2 - Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
In this problem: We start with the first digit \(2\). Since \(14\) does not fit into \(2\), we include more digits from the left to make \(28\). Then we repeat: divide, multiply, subtract, bring down. The lettered steps below run through this cycle one turn at a time.
| 14 | 2 | 8 | 5 | 6 |
Step 2a
Step 2a - Check whether the divisor fits into the digits taken so far. If it does not, include the next digit from the dividend.
In this problem: We look at \(2\). \(14\) does not fit yet, so we include the next digit \(8\) to make \(28\).
| 14 | 2 | 8 | 5 | 6 |
Step 2b
Step 2b - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(28\). \(14\) fits \(2\) times. Multiply: \(14 \times 2 = 28\). Subtract: \(28 - 28 = 0\).
| 2 | ||||
| 14 | 2 | 8 | 5 | 6 |
| - | 2 | 8 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(8 - 8 = 0\) → write \(0\) under the ones column.
| 2 | 8 | |
| − | 2 | 8 |
| 0 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(2 - 2 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 2 | 8 | |
| − | 2 | 8 |
| 0 | ||
Final Answer
Step 2c
Step 2c - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(5\) next to the remainder \(0\). Now we have \(5\) to work with.
| 2 | ||||
| 14 | 2 | 8 | 5 | 6 |
| - | 2 | 8 | ||
| 0 | 5 |
Step 2d
Step 2d - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(5\). \(14\) does not fit, so we write \(0\) on top. The remainder stays \(5\).
| 2 | 0 | |||
| 14 | 2 | 8 | 5 | 6 |
| - | 2 | 8 | ||
| 0 | 5 | |||
| 5 |
Step 2e
Step 2e - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(6\) next to the remainder \(5\). Now we have \(56\) to work with.
| 2 | 0 | |||
| 14 | 2 | 8 | 5 | 6 |
| - | 2 | 8 | ||
| 0 | 5 | |||
| 5 | 6 |
Step 2f
Step 2f - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(56\). \(14\) fits \(4\) times. Multiply: \(14 \times 4 = 56\). Subtract: \(56 - 56 = 0\).
| 2 | 0 | 4 | ||
| 14 | 2 | 8 | 5 | 6 |
| - | 2 | 8 | ||
| 0 | 5 | |||
| 5 | 6 | |||
| - | 5 | 6 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(6 - 6 = 0\) → write \(0\) under the ones column.
| 5 | 6 | |
| − | 5 | 6 |
| 0 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(5 - 5 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 5 | 6 | |
| − | 5 | 6 |
| 0 | ||
Final Answer
Final Answer
See Example 4 Hide Example 4
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
In this problem: We divide \(936\) by \(3\). The quotient goes on top, and we work from left to right.
| 3 | 9 | 3 | 6 |
Step 2
Step 2 - Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
In this problem: We start with the first digit \(9\) because it is big enough to divide by \(3\). Then we repeat: divide, multiply, subtract, bring down. The lettered steps below run through this cycle one turn at a time.
| 3 | 9 | 3 | 6 |
Step 2a
Step 2a - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(9\). \(3\) fits \(3\) times. Multiply: \(3 \times 3 = 9\). Subtract: \(9 - 9 = 0\).
| 3 | |||
| 3 | 9 | 3 | 6 |
| - | 9 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(9 - 9 = 0\) → write \(0\) under the ones column.
| 9 | |
| − | 9 |
| 0 | |
Final Answer
Step 2b
Step 2b - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(3\) next to the remainder \(0\). Now we have \(3\) to work with.
| 3 | |||
| 3 | 9 | 3 | 6 |
| - | 9 | ||
| 0 | 3 |
Step 2c
Step 2c - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(3\). \(3\) fits \(1\) time. Multiply: \(3 \times 1 = 3\). Subtract: \(3 - 3 = 0\).
| 3 | 1 | ||
| 3 | 9 | 3 | 6 |
| - | 9 | ||
| 0 | 3 | ||
| - | 3 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(3 - 3 = 0\) → write \(0\) under the ones column.
| 3 | |
| − | 3 |
| 0 | |
Final Answer
Step 2d
Step 2d - Bring down the next digit of the dividend and place it beside the remainder.
In this problem: We bring down the next digit \(6\) next to the remainder \(0\). Now we have \(6\) to work with.
| 3 | 1 | ||
| 3 | 9 | 3 | 6 |
| - | 9 | ||
| 0 | 3 | ||
| - | 3 | ||
| 0 | 6 |
Step 2e
Step 2e - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(6\). \(3\) fits \(2\) times. Multiply: \(3 \times 2 = 6\). Subtract: \(6 - 6 = 0\).
| 3 | 1 | 2 | |
| 3 | 9 | 3 | 6 |
| - | 9 | ||
| 0 | 3 | ||
| - | 3 | ||
| 0 | 6 | ||
| - | 6 | ||
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(6 - 6 = 0\) → write \(0\) under the ones column.
| 6 | |
| − | 6 |
| 0 | |
Final Answer
Final Answer