There, we studied a problem on long division of a Three digit number by a two digit number.

Here, we extend that study by solving Long Division of a Four digit number by a two digit number. We also introduce long division by three digit numbers.

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Step1 : Here the divisor is a two digit number, 37. So we see the first two digits of the dividend which is 58. We have to find how many times 37 divides 58.

1 x 37 = 37; 2 x 37 is more than 2 x 30 i.e. 60 > 58. So 37 divided 58 one time.

We have 1 x 37 = 37. We put 1 in the right bracket and 37 below 58 of the dividend. 37 subtracted from 58 gives 21.

Dividend
Divisor 37 ) 5892 ( 1
37
-----
21

Step2 : We descend the next digit of the dividend, 9 to the right of 21 to make it 219. 37 is near 40 and we know 5 x 40 = 200 which is near 219. Let us find 5 x 37 and 6 x 37.

37
5
--- ^{3}
185
---

37
6
--- ^{4}
222
---

6 x 37 = 222 exceeds 219. So 37 divides 219, five times and 5 x 37 = 185. We write 5 in the right bracket after 1 and 185 below 219. 185 subtracted from 219 gives 34.

Step3 : Teaching Long Division We descend the next (last) digit of the dividend, 2 to the right of 34 to make it 342. 37 is near 40 and we know 8 x 40 = 320 which is near 342. Let us find 8 x 37 and 9 x 37.

37
8
--- ^{5}
296
---

37
9
--- ^{6}
333
---

9 x 37 = 333 is less than 342. So 37 divides 342, nine times and 9 x 37 = 333. We write 9 in the right bracket after 15 and 333 below 342. 333 subtracted from 342 gives 9 which is the remainder.

As the number of digits of the dividend increases, the number of steps in the process increases. Except for that the procedure is same.

Teaching Long Division is done by the above three steps.

Let us see another example in which a six digit number is divided by a three digit number.

Example 2 of Teaching Long Division

Divide 609182 by 463.

Solution :

Step1:Teaching Long Division Here the divisor is a three digit number 463. So we see the first three digits of the dividend which is 609. We have to find how many times 463 divides 609. 1 x 463 = 463; 2 x 463 is more than 800 > 609. So 463 divides 609 one time.

We have 1 x 463 = 463. We put 1 in the right bracket and 463 below 609 of the dividend. 463 subtracted from 609 gives 146.

Dividend
Divisor 463 ) 609182 ( 1
463
---
146

Step2: Teaching Long Division We descend the next digit of the dividend, 1 to the right of 146 to make it 1461. 463 is near 500 and we know 3 x 500 = 1500 which is near 1461. Let us find 3 x 463.

463
3
---- ^{1}
1389
----

4 x 463 is more than 1600 which exceeds 1461. So 463 divides 1461, three times and 3 x 463 = 1389. We write 3 in the right bracket after 1 and 1389 below 1461. 1389 subtracted from 1461 gives 72.

Step3: Teaching Long Division We descend the next digit of the dividend, 8 to the right of 72 to make it 728. 1 x 463 = 463; 2 x 463 is more than 800 > 728. So 463 divides 728 one time.

We have 1 x 463 = 463. We put 1 in the right bracket after 13 and 463 below 728. 463 subtracted from 728 gives 265.

Step4: Teaching Long Division We descend the next (last) digit of the dividend, 2 to the right of 265 to make it 2652. 463 is near 500 and we know 5 x 500 = 2500 which is near 2652. Let us find 5 x 463 and 6 x 463.

463
5
---- ^{1}^{3}
2315
----

463
6
---- ^{1}^{3}
2778
----

6 x 463 = 2778 exceeds 2652. So 463 divides 2652, five times and 5 x 463 = 2315. We write 5 in the right bracket after 131 and 2315 below 2652. 2315 subtracted from 2652 gives 337 which is the remainder.

Thus, with any Dividend and any Divisor, we can carry out the division by following the same procedure.

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Solve the following problems on Teaching Long Division

Find the quotient and the remainder in the following divisions. Also check your results.

73651 ÷ 742

827346 ÷ 876

1642012 ÷ 1021

47013 ÷ 271

793097 ÷ 465

For Answers see at the bottom of the page.

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