**Division Algorithm Worksheet : **

Worksheet given in this section will be much useful for the students who would like to practice problems on division algorithm.

**Problem 1 :**

Divide 300 by 7, list out dividend, divisor, quotient, remainder and write division algorithm.

**Problem 2 :**

Divide 258 by 9, list out dividend, divisor, quotient, remainder and write division algorithm.

**Problem 3 :**

Divide 400 by 8, list out dividend, divisor, quotient, remainder and write division algorithm.

**Problem 4 :**

Divide 1675 by 13, list out dividend, divisor, quotient, remainder and write division algorithm.

**Problem 5 :**

What is dividend, when divisor is 17, the quotient is 9 and the remainder is 5 ?

**Problem 6 :**

When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?

**Problem 7 :**

On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor ?

**Problem 8 :**

On dividing a certain number by 342, we get 47 as remainder. If the same number is divided by 18, what will be the remainder ?

**Problem 1 :**

Divide 300 by 7, list out dividend, divisor, quotient, remainder and write division algorithm.

**Solution :**

Let us divide 300 by 7 using long division as given below.

From the above long division, we have

Dividend = 300

Divisor = 7

Quotient = 42

Remainder = 6

Division algorithm for the above division :

**Problem 2 :**

Divide 258 by 9, list out dividend, divisor, quotient, remainder and write division algorithm.

**Solution :**

As we have seen in problem 1, if we divide 258 by 9 using long division, we get

Dividend = 258

Divisor = 9

Quotient = 28

Remainder = 6

Division algorithm for the above division is

258 = 28x9 + 6

**Problem 3 :**

Divide 400 by 8, list out dividend, divisor, quotient, remainder and write division algorithm.

**Solution :**

As we have seen in problem 1, if we divide 400 by 8 using long division, we get

Dividend = 400

Divisor = 8

Quotient = 50

Remainder = 0

Division algorithm for the above division is

400 = 50x8 + 0

**Problem 4 :**

Divide 1675 by 13, list out dividend, divisor, quotient, remainder and write division algorithm.

**Solution :**

As we have seen in problem 1, if we divide 1675 by 13 using long division, we get

Dividend = 1675

Divisor = 13

Quotient = 128

Remainder = 11

Division algorithm for the above division is

1675 = 128x13 + 11

**Problem 5 :**

What is dividend, when divisor is 17, the quotient is 9 and the remainder is 5 ?

**Solution :**

Using division algorithm

Dividend = Divisor x quotient + Remainder

Dividend = 17 x 9 + 5

Dividend = 153 + 5

Dividend = 158

So, the dividend is 158.

**Problem 6 :**

When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?

**Solution :**

Using division algorithm

Dividend = Divisor x quotient + Remainder

From the given information, we have

n = 8q + 3

To find the remainder, when 6n is divided by 8, we multiply 6 on both sides.

6n = 48q + 18

6n = 48q + 16 + 2

Factoring out 8 from 48 and 16, we get

6n = 8(6q + 2) + 2

8(6q + 2) is the multiple of 8 and remainder is 2.

So, we get 2 as remainder when dividing 6n by 8.

**Problem 7 :**

On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor ?

**Solution :**

Let x be the divisor.

Dividend = 12401, divisor = x, quotient = 76 and remainder = 13.

12401 = 76x + 13

12401 - 13 = 76x

Solving for x, we get the divisor.

76x = 12388

x = 12388/76

x = 163

So, the divisor is 163.

**Problem 8 :**

On dividing a certain number by 342, we get 47 as remainder. If the same number is divided by 18, what will be the remainder ?

**Solution :**

Let x be the quotient on dividing a number by 342, which yields the remainder 47.

By applying the above information in division algorithm, we get

Number = 342x + 47

Now, we should divide the same number by 18 and find the remainder.

Representing 342x + 47 as the multiple of 18, we get

342x + 47 = (18 ⋅ 19x) + 36 + 11

342x + 47 = (18 ⋅ 19x) + 2 ⋅ 18 + 11

Factoring out 18, we get

342x + 47 = 18(19x + 2) + 11

18(19x + 2) is the multiple of 18.

So, the remainder is 11.

After having gone through the stuff given above, we hope that the students would have understood how to solve problems using division algorithm.

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