# DIVISION ALGORITHM PROBLEMS AND SOLUTIONS

Division Algorithm Problems and Solutions :

In this section, we are going to see some practice questions on division algorithm.

When we divide a number by another number, the division  algorithm is, the sum of product of quotient & divisor and remainder is equal to dividend.

More clearly,

Dividend  = Quotient x Divisor + Remainder

When we divide a number by another number, we will have the terms dividend, divisor, quotient and remainder.

• The number which we divide is called the dividend.
• The number by which we divide is called the divisor.
• The result obtained is called the quotient.
• The number left over is called the remainder.

More clearly, Division Algorithm : ## Division Algorithm Problems and Solutions

Question 1 :

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

(A)  153  (B)  156  (C)  158  (D)  None of these

Solution :

Using division algorithm

Dividend  =  Divisor x quotient + Remainder

Dividend  =  17 x 9 + 5

Dividend  =  153 + 5

Dividend  =  158

Hence the required dividend is 158.

Question 2 :

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

A) 0     B) 1     C) 2     D) 3     E) 4

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.

Hence we get 2 as remainder, while dividing 6n by 8.

Question 3 :

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

Hence the divisor is 163.

Question 4 :

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.

Hence the remainder is 11.

Question 5 :

If a positive integer n is divided by 5, the remainder is 3. Which of the numbers below yields a remainder of 0 when it is divided by 5 ?

A) n + 3     B) n + 2     C) n - 1     D) n - 2     E) n + 1

Solution :

It can be solved easily by doing a small assumption.

If n = 8 It is possible for all values of n which is divisible by 5 and more than 3.If we add 2 by n, we will get the remainder as 0.

Hence the answer is n + 2.

Note :

Using the concept division algorithm, we may solve this problem. 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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