When a number is divided by 296, the remainder is 75. What will be the remainder when the same number is divided by 37?
- A1
- B19
- C23
- D12
Solution & Step-by-step Explanation
Let the number be represented as:
N=296k+75
where k is an integer quotient.
We want to find the remainder when N is divided by 37:
37
N
=
37
296k+75
Since 296 is completely divisible by 37 (37×8=296), the term 296k leaves a remainder of 0.
Therefore, the remainder depends entirely on dividing 75 by 37:
75=37×2+1
The remainder is 1.
N=296k+75
where k is an integer quotient.
We want to find the remainder when N is divided by 37:
37
N
=
37
296k+75
Since 296 is completely divisible by 37 (37×8=296), the term 296k leaves a remainder of 0.
Therefore, the remainder depends entirely on dividing 75 by 37:
75=37×2+1
The remainder is 1.