**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.

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