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.
More clearly, Division Algorithm :
Problem 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.
Problem 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.
Problem 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.
Problem 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.
Problem 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.
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