# Long Division

As we know that the division is to distribute a given value or quantity into groups having equal values. In long division, values at the individual place (Thousands, Hundreds, Tens, Ones) are dividend one at a time starting with the highest place.

Division of 2 Digit Number by 1 Digit Number:

Division can be shown in two ways. e.g. Short form and Long form.

 Short forms of division - Long forms of division -

A. Division by One-Digit Divisor

1. Divide 27 by 9

Solution:

Let us divide.

 Step I: Write 27 inside the bracket and 9 on the left side of the bracket.Step II: Start division from left to right, that is, divide 2 by 9. Since, we cannot divide 2 by 9 so, we will divide 27 by 9.Step III: Recall the table of 9.9 × 3 = 27Now, write 3 in the quotient and subtract 27 from 27. The result is 0.Thus, 27 ÷ 9 = 3

2. Divide 92 by 4

Solution:

Let us divide.

 Step I: Write 92 inside the bracket and 4 on the left side of the bracket.Step II: Start division from left to right, that is, divide 9 tens by 4. 4 × 2 = 84 × 3 = 1212 tens is bigger than 9 tens, so we take 4 × 2 = 8 tens.Step III: Write 2 in the quotient.Step IV: Subtract 8 from 9 and get 1 as remainder.Step V: Bring down 2 from ones place and write it to the right of 1. 12 is the new dividend.Step VI: Write 3 in the quotient and subtract 12 from 12. The result is 0. Thus, 92÷4 = 23

3. Divide 36 by 3.

 3 × 1 = 3Write 1 as a quotient write 3 under 3 and subtract Bring down 6 ones.Now divide 6 by 33 × 2 = 6Write 2 as a quotient andwrite 6 under the new dividend and subtractNow, 36 divided by 3 is 12.

4. Divide 30 by 5.

 Read the table of 5We find 5 × 6 = 30Now we know 5 is divisor 6 isquotient and  30 is dividend.

Notes:

I. Divide the Tens.

II. Then, divide the Ones.

B. Division of 3-Digit Number by One-Digit Number:

1. Divide 324 by 2.

First Divide the Hundreds

 Dividing HundredsDivide 6 H by 2 = 3H write 3 in place of quotient and 6 under 6 and subtract 6 - 6=0

Then, Divide the Tens.

 Dividing TensNow, bring down 4 T. Divide 4 T by 2 = 2T write 2 in tens place of the quotient and 4 under 4 then subtract 4 - 4 = 0

Finally, Divide the Ones.

 Dividing OnesBring down 8 Ones. Divide 8 ones by 2 = 4 ones write 4 in the ones place of the quotient. write 8 under 8 and subtract8 - 8 = 0

D. Division of 4-Digits Number by 1-Digit Number:

To divide 4-Digit numbers follow these steps -

(i) Divide the Thousands.

(ii) Divide the Hundreds.

(iii) Divide the Tens.

(iv) Divide the Ones.

1. Divide 3693 by 3.

 Step I: Dividing ThousandsDivide 3 Th by 3 = 1Thwrite 1 in place of quotient and 3 under 3 andsubtract 3 - 3 =0  Step II: Dividing HundredsBring down 6 H.Divide 6 H by 3 = 2Hwrite 2 in place of quotient and 6 under 6 andsubtract 6 - 6=0  Step III: Dividing TensNow, bring down 9 T.Divide 9 T by 3 = 3Twrite 3 in tens place of the quotient and 9 under 9then subtract 9 - 9 = 0 Step IV: Dividing OnesBring down 3 Ones.Divide 3 ones by 3 = 1 oneswrite 1 in the ones place of the quotient.write 3 under 3 and subtract3 - 3 = 0

2. Divide 6428 by 2.

 Step I: Dividing ThousandsDivide 6 Th by 2 = 3Thwrite 3 in place of quotient and 6 under 6 andsubtract 6 - 6 =0  Step II: Dividing HundredsBring down 4 H.Divide 4 H by 2 = 2Hwrite 2 in place of quotient and 4 under 4 andsubtract 4 - 4=0  Step III: Dividing TensNow, bring down 2 T.Divide 2 T by 2 = 1Twrite 1 in tens place of the quotient and 2 under 2then subtract 2 - 2 = 0 Step IV: Dividing OnesBring down 8 Ones.Divide 8 ones by 2 = 4 oneswrite 4 in the ones place of the quotient.write 8 under 8 and subtract8 - 8 = 0

Division with Remainder:

1. Divide 49 by 4.

 T: 4 ÷ 4 = 1.Quotient = 1O: 9 ÷ 4= ?4 × 2 = 8 (nearest number)9 - 8 = 1So, Quotient = 2    Remainder = 1

Divisor - 4, Quotient - 12, Remainder - 1.

2. Find the quotient and remainder of 649 ÷ 9.

Solution:

 Step I: We start dividing the hundreds first. Since 6 hundreds cannot be divided into 9 groups of hundreds, the quotient at hundreds column is zero.Step II: 6 Hundreds are now changed into 60 tens and added to 4 tens, making 64 tens.Step III: 64 tens give 9 groups of 7 tens each and 1 ten is left over.Step IV: 1 ten give 10 ones, 10 ones + 9 ones = 19 onesStep V: 19 ones can be put into 2 groups of 9 and 1 one is left over. q = 72; r = 1

3. Divide 697 by 3.

 H: 6 ÷ 3 = 2. T: 9 ÷ 3 = 3.O: 7 ÷ 3 = ?     3 × 2 = 6 (nearest number)      7 - 6 = 1So, in O Quotient = 2         Remainder = 1

Divisor - 3, Quotient - 232, Remainder 1.

4. Divide 8643 by 2.

 Th: 8 ÷ 2 = 4H: 6 ÷ 2 = 3T: 4 ÷ 2 = 2O: 3 ÷ 2 = ?     2 × 1 = 2     3 - 2 = 1So. in O Quotient = 2          Remainder = 1

Divisor - 2, Quotient - 4321, Remainder 1.

5. Divide 6609 by 6.

 Th: 6 ÷ 6 = 1H: 6 ÷ 6 = 1T: 0 ÷ 6 = 0O: 9 ÷ 6 = ?     6 × 1 = 6     9 - 6 = 3So, in Quotient = 1      Remainder = 3

Divisor - 6, Quotient - 1101, Remainder 3.

E. Division with Regrouping:

1. Divide 96 by 4.

 Step I: Dividing TensDivide 9 ÷ 4 = ?4 × 2 = 8           8 < 94 × 3 = 12       12 > 9we use 4 × 2 = 8.write 2 in tens place of the quotient and 8 below 9 then subtract 9 - 8 = 1
 Step II: Dividing OnesBring down 6 Ones,we have 16 ones 1 ten+ 6 ones. Divide 16 ones ÷ 44 × 4 = 16write 4 in ones place of the quotient and 16 below 16Now, 16 - 16 = 0

2. Divide 736 by 3.

 H: 7 ÷ 3 = ?.   So, 3 × 2 =6Q: 2;   R: 7 - 6 = 1 or 1 hundreds Regroup - 1 hundreds and 3 tens = 13 tensT: 13 + 3 = ?. So, 3 × 4 = 12Q: 4;    R: 13 - 12 = 1 or 1 tens Regroup - 1 tens and 5 ones = 15 onesO: 16 ÷ 3 = ?.   So, 3 × 5 = 15Q: 5;   R: 16 - 15 = 1 Remainder - 1

Here 3 is divisor, 736 is dividend, 245 is quotient and 1 is remainder.

3. Divide 3373 by 4.

 Th: 3 < 4 so 3 + 4 is not possible. Regroup - 3 thousands and 3 hundreds = 33 hundredsH﻿:33 ÷ 4 = ?Q: 8;      R: 33 - 32 = 1 Remainder - 1 hundreds Regroup - 1 hundreds and 7 tens = 17 tensT: 17 ÷ 4 = 4Q: 4     R: 17 - 16 = 1    Remainder - 1 tensRegroup - 1 tens and 3 ones = 13 onesO:13 ÷ 4 = 3Q: 3     R: 13 - 12 = 1    Remainder - 1

Here 4 is divisor, 3373 is dividend, 845 is quotient and 1 is remainder.

Keep in Mind

• First, divide the Thousands.
• Then, divide the Hundreds. Then, divide the Tens.
• Finally, divide the Ones.

Division by Two-Digit Divisors

1. Divide 2698 by 21.

Solution:

Recall the process of long division.

 Step I: 2 thousands cannot be divided into 21 groups of thousand. So, 0 is placed as quotient in the thousands column.Step II: 2 thousands give 20 hundreds.20 hundreds + 6 hundreds give 26 hundreds. 26 hundreds make 1 group of 21 hundreds. 5 hundreds are left.Step III: 5 hundreds give 50 tens. q = 128; r = 10

So, 50 tens + 9 tens = 59 tens

59 tens are to be divided into 21 groups of tens

59 tens ÷ 21 makes 2 groups with 17 tens left.

2 is placed in the quotient in the tens column.

Step IV: 17 tens = 170 ones

170 ones + 8 ones = 178 ones

178 ones ÷ 21 makes 8 groups with 10 ones left.

Thus, in division of 2,698 by 21, we get 128 as quotient and 10 as remainder.

Word Problems on Long Division:

To solve any word problem, we need to read each word carefully and select numbers carefully from the question to solve it.

1. If 60 cookies to be put in 5 packets, how many cookies will be packed in one packet?

 Solution:Number of cookies = 60 cookiesEqually distributed in 5 packetsNumber of cookies in one packet = 60 ÷ 5

Thus, 12 cookies will be packed in one packet.

Questions and Answers on Long Division:

A. Division of 2 Digit Number by 1 Digit Number:

I. Divide and find the quotient:

(i) 85 ÷ 5 = _____

(ii) 54 ÷ 3 = _____

(iii) 63 ÷ 7 = _____

(iv) 60 ÷ 3 = _____

(v) 42 ÷6 = _____

(vi) 32 ÷ 8 = _____

(vii) 88 ÷ 8 = _____

(viii) 69 ÷ 3 = _____

(ix) 48 ÷ 3 = _____

(x) 42 ÷ 6 = _____

(xi) 68 ÷ 4 = _____

(xii) 96 ÷ 6 = _____

(xiii) 86 ÷ 2 = _____

(xiv) 36 ÷ 9 = _____

(xv) 77 ÷ 7 = _____

(xvi) 63 ÷ 3 = _____

(xvii) 22 ÷ 2 = _____

(xviii) 72 ÷ 9 = _____

(xix) 33 ÷ 3 = _____

(xx) 68 ÷ 2 = _____

I. (i) 17

(ii) 18

(iii) 9

(iv) 20

(v) 7

(vi) 4

(vii) 11

(viii) 23

(ix) 16

(x) 7

(xi) 17

(xii) 16

(xiii) 43

(xiv) 4

(xv) 11

(xvi) 21

(xvii) 11

(xviii) 8

(xix) 11

(xx) 34

II. Find the quotient:

 (i) 3 |$$\overline{2 7}$$ (ii) 7 |$$\overline{4 2}$$
 (iii) 8 |$$\overline{6 4}$$ (iv) 2 |$$\overline{1 8}$$
 (v) 3 |$$\overline{2 1}$$ (vi) 9 |$$\overline{8 1}$$
 (vii) 5 |$$\overline{3 5}$$ (viii) 6 |$$\overline{4 8}$$
 (ix) 4 |$$\overline{3 6}$$ (x) 7 |$$\overline{6 3}$$
 (xi) 3 |$$\overline{9 3}$$ (xii) 2 |$$\overline{8 2}$$
 (xiii) 2 |$$\overline{2 6}$$ (xiv) 2 |$$\overline{1 0}$$
 (xv) 3 |$$\overline{3 0}$$ (xvi) 7 |$$\overline{4 9}$$
 (xvii) 2 |$$\overline{6 4}$$ (xviii) 8 |$$\overline{7 2}$$
 (xix) 7 |$$\overline{7 7}$$ (xx) 8 |$$\overline{4 8}$$

II. (i) 9

(ii) 6

(iii) 8

(iv) 9

(v) 7

(vi) 9

(vii) 7

(viii) 8

(ix) 9

(x) 9

(xi) 31

(xii) 41

(xiii) 13

(xiv) 5

(xv) 10

(xvi) 7

(xvii) 32

(xviii) 9

(xix) 11

(xx) 6

B. Division of 3-Digit Number by 1-Digit Number:

III. Divide and find the quotients -

(i) 246 ÷ 2 = _____

(ii) 666 ÷ 6 = _____

(iii) 339 ÷ 3 = _____

(iv) 936 ÷ 3 = _____

(v) 648 ÷ 2 = _____

(vi) 222 ÷ 2 = _____

(vii) 242 ÷ 2 = _____

(viii) 777 ÷ 7 = _____

(ix) 480 ÷ 2 = _____

(x) 420 ÷ 2 = _____

(xi) 848 ÷ 2 = _____

(xii) 399 ÷ 3 = _____

(xiii) 448 ÷ 4 = _____

(xiv) 224 ÷ 2 = _____

(xv) 960 ÷ 3 = _____

(xvi) 848 ÷ 4 = _____

(xvii) 402 ÷ 2 = _____

(xviii) 636 ÷ 3 = _____

(xix) 939 ÷ 3 = _____

(xx) 444 ÷ 4 = _____

III. (i) 123

(ii) 111

(iii) 113

(iv) 312

(v) 324

(vi) 111

(vii) 121

(viii) 111

(ix) 240

(x) 210

(xi) 424

(xii) 133

(xiii) 112

(xiv) 112

(xv) 320

(xvi) 212

(xvii) 201

(xviii) 212

(xix) 313

(xx) 111

IV. Find the quotient:

 (i) 4 |$$\overline{804}$$ (ii) 3 |$$\overline{363}$$
 (iii) 4 |$$\overline{408}$$ (iv) 2 |$$\overline{826}$$
 (v) 2 |$$\overline{604}$$ (vi) 3 |$$\overline{336}$$
 (vii) 8 |$$\overline{888}$$ (viii) 4 |$$\overline{484}$$
 (ix) 3 |$$\overline{993}$$ (x) 4 |$$\overline{884}$$
 (xi) 5 |$$\overline{555}$$ (xii) 2 |$$\overline{484}$$
 (xiii) 3 |$$\overline{366}$$ (xiv) 2 |$$\overline{442}$$
 (xv) 2 |$$\overline{882}$$ (xvi) 3 |$$\overline{663}$$
 (xvii) 2 |$$\overline{866}$$ (xviii) 9 |$$\overline{999}$$
 (xix) 2 |$$\overline{224}$$ (xx) 3 |$$\overline{333}$$

IV. (i) 201

(ii) 121

(iii) 102

(iv) 413

(v) 302

(vi) 112

(vii) 111

(viii) 121

(ix) 331

(x) 221

(xi) 111

(xii) 242

(xiii) 122

(xiv) 221

(xv) 441

(xvi) 221

(xvii) 433

(xviii) 111

(xix) 112

(xx) 111

C. Division of 4-Digit Number by 1-Digit Number:

V. Divide and find the quotients -

(i) 7777 ÷ 7 = _____

(ii) 4884 ÷ 2 = _____

(iii) 6699 ÷ 3 = _____

(iv) 9999 ÷ 3 = _____

(v) 6666 ÷ 2 = _____

(vi) 9969 ÷ 3 = _____

(vii) 4002 ÷ 2 = _____

(viii) 2468 ÷ 2 = _____

(ix) 4884 ÷ 4 = _____

(x) 6844 ÷ 2 = _____

(xi) 2244 ÷ 2 = _____

(xii) 6969 ÷ 3 = _____

(xiii) 8844 ÷ 2 = _____

(xiv) 8084 ÷ 4 = _____

(xv) 6060 ÷ 3 = _____

(xvi) 4444 ÷ 2 = _____

(xvii) 6448 ÷ 2 = _____

(xviii) 9060 ÷ 3 = _____

(xix) 4488 ÷ = _____

(xx) 6666 ÷ 3 = _____

(xxi) 8888 ÷ 4 = _____

(xxii) 8888 ÷ 2  = _____

(xxiii) 9966 ÷ 3 = _____

(xxiv) 4488 ÷ 4 = _____

VI. Find the Quotient:

 (i) 2 |$$\overline{2424}$$ (ii) 3 |$$\overline{3939}$$
 (iii) 4 |$$\overline{8484}$$ (iv) 2 |$$\overline{4242}$$
 (v) 5 |$$\overline{5505}$$ (vi) 8 |$$\overline{4848}$$
 (vii) 7 |$$\overline{4956}$$ (viii) 9 |$$\overline{8136}$$
 (ix) 2 |$$\overline{2826}$$ (x) 3 |$$\overline{3639}$$
 (xi) 2 |$$\overline{8448}$$ (xii) 3 |$$\overline{3036}$$
 (xiii) 2 |$$\overline{8468}$$ (xiv) 4 |$$\overline{8448}$$
 (xv) 3 |$$\overline{3363}$$ (xvi) 6 |$$\overline{6636}$$

D. Division with Remainder:

VII. Divide and find the quotients and remainders -

(i) 96 ÷ 3 = _____

(ii) 89 ÷ 4 = _____

(iii) 45 ÷ 4 = _____

(iv) 65 ÷ 2 = _____

(v) 37 ÷ 3 = _____

(vi) 63 ÷ 2 = _____

(vii) 27 ÷ 4 = _____

(viii) 95 ÷ 3 = _____

(ix) 849 ÷ 4 = _____

(x) 807 ÷ 4 = _____

(xi) 847 ÷ 4 = _____

(xii) 638 ÷ 3 = _____

(xiii) 4849 ÷ 2 = _____

(xiv) 2427 ÷ 2 = _____

(xv) 9634 ÷ 3 = _____

(xvi) 4846 ÷ 4 = _____

(xvii) 8485 ÷ 4 = _____

(xviii) 6937 ÷ 3 = _____

(xix) 5556 ÷ 5 = _____

(xx) 9695 ÷ 3 = _____

VIII. Find the Quotients and remainders:

 (i) 2 |$$\overline{25}$$ (ii) 4 |$$\overline{87}$$
 (iii) 6 |$$\overline{669}$$ (iv) 2 |$$\overline{889}$$
 (v) 3 |$$\overline{965}$$ (vi) 3 |$$\overline{397}$$
 (vii) 4 |$$\overline{849}$$ (viii) 5 |$$\overline{556}$$
 (ix) 2 |$$\overline{245}$$ (x) 3 |$$\overline{668}$$
 (xi) 2 |$$\overline{667}$$ (xii) 2 |$$\overline{887}$$
 (xiii) 3 |$$\overline{6968}$$ (xiv) 2 |$$\overline{4829}$$
 (xv) 4 |$$\overline{4889}$$ (xvi) 2 |$$\overline{8267}$$

D. Division with Regrouping:

IX. Find the quotients and remainders of these sums -

(i) 84 ÷ 7 = _____

(ii) 96 ÷ 5 = _____

(iii) 99 ÷ 8 = _____

(iv) 81 ÷ 3 = _____

(v) 76 ÷ 4 = _____

(vi) 53 ÷ 2 = _____

(vii) 95 ÷ 4 = _____

(viii) 67 ÷ 5 = _____

(ix) 711 ÷ 9 = _____

(x) 207 ÷ 3 = _____

(xi) 776 ÷ 8 = _____

(xii) 441 ÷ 7 = _____

(xiii) 920 ÷ 8 = _____

(xiv) 607 ÷ 5 = _____

(xv) 534 ÷ 5 = _____

(xvi) 7284 ÷ 3 = _____

(xvii) 2389 ÷ 4 = _____

(xviii) 6700 ÷ 9 = _____

(xix) 8489 ÷ 7 = _____

(xx) 9900 ÷ 8 = _____

X. Find the Quotients and remainders:

 (i) 3 |$$\overline{57}$$ (ii) 4 |$$\overline{62}$$
 (iii) 5 |$$\overline{77}$$ (iv) 4 |$$\overline{68}$$
 (v) 7 |$$\overline{85}$$ (vi) 2 |$$\overline{314}$$
 (vii) 4 |$$\overline{973}$$ (viii) 5 |$$\overline{630}$$
 (ix) 6 |$$\overline{746}$$ (x) 5 |$$\overline{6795}$$
 (xi) 7 |$$\overline{9395}$$ (xii) 8 |$$\overline{9985}$$

II. Solve the given word problems on long division.

1. Shelly has 75 pencils. She shares them between her 5 friends. How many pencils will each of her friend get?

2. In class III, there are total 70 children. If there are 5 sections in class III, how many children are there in each section?

3. There are 68 birds in a zoo in 4 cages. How many birds are there in each cage?

4. Jack, the clown has 99 balloons which he needs to share between 9 children at the fair. How many balloons does each child get?

5. Nancy has 96 pieces of candy. She has 8 bags. She wants to put the same amount of candies in each bag. How many will she put in each bag?

6. Mike organised 24 chairs in 4 rows for a party. How many chairs are there in each row?

7. You have 60 gum balls that you need to share equally in five containers. How many gum balls will be in each container?

8. There are 96 books on the shelf. If the books are to be shared equally amongst 4 table groups in the class, how many books will be there on each table?

II. 1. 15

2. 14

3. 17

4. 11

5. 12

6. 6

7. 12

8. 24

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