To solve this problem first we need to know the formula:
Dividend= Divisor × Quotient+ Remainder
Let's understand the terms first so as not to get confused by them:
Dividend: the number which you are dividing.
Divisor: the number you are are dividing by.
Quotient: Answer that you get after division is complete.
Remainder: The number that is leftover after dividing.

Let's take an example to get hold of the terms better:
E.g→ 54÷7
Here:
Dividend: 54
Divisor: 7
Quotient: 7
Remainder: 5

Now,in the above Question it is asked to find such a number that after dividing it by -3 we will get the Quotient as 35 and the remainder as 2.
Let's classify them among the four terms:-
Here:
We have to find out the dividend.
So let the dividend be X.
Dividend= X
Divisor= -3
Quotient=35
Remainder=2
Formula:-
Dividend= Divisor × Quotient+ Remainder
Let's Substitute the values:
Dividend= Divisor × Quotient+ Remainder
X=(-3)×35+2
X= (-105)+2
X= -103
So the Dividend here is (-103).
On dividing (-103) by (-3) we will get the quotient as 35 and remainder as 2.

Understanding the Problem
To find the integer that when divided by -3 gives a quotient of 35 and a remainder of 2, we need to use the formula:
Dividend = Divisor × Quotient + Remainder

Solution
- Let's denote the integer as X.
- According to the problem, when X is divided by -3, the quotient is 35 and the remainder is 2.
- Using the formula mentioned above, we can write the equation as: X = -3 × 35 + 2
- Solving the equation: X = -105 + 2
- X = -103
Therefore, the integer we are looking for is -103. When -103 is divided by -3, it gives a quotient of 35 and a remainder of 2.

Final Answer
The integer we are looking for is -103.