If a perfect square, not divisible by 6, be divided by 6, the remainder will be

Options

A. 1, 3 or 5
B. 1, 2 or 5
C. 1, 3 or 4
D. 1, 2 or 4

Answer

To solve the problem, we need to determine the possible remainders when a perfect square that is not divisible by 6 is divided by 6.

### Step-by-Step Solution:

1. **Understanding Perfect Squares**:
A perfect square is a number that can be expressed as the square of an integer. Examples include 0, 1, 4, 9, 16, 25, etc.

2. **Divisibility by 6**:
A number is divisible by 6 if it is divisible by both 2 and 3. Therefore, we need to find perfect squares that are not divisible by 6.

3. **Finding Perfect Squares Not Divisible by 6**:
- Perfect squares can be classified based on their residues when divided by 6.
- The possible residues of perfect squares modulo 6 are 0, 1, 3, and 4.

4. **Analyzing Each Case**:
- **Residue 0**: Perfect squares like \(0^2\) (0) are divisible by 6.
- **Residue 1**: Perfect squares like \(1^2\) (1) are not divisible by 6.
- **Residue 3**: Perfect squares like \(3^2\) (9) are not divisible by 6.
- **Residue 4**: Perfect squares like \(2^2\) (4) are not divisible by 6.

5. **Conclusion**:
Since we are looking for perfect squares that are not divisible by 6, we only consider the residues 1, 3, and 4.
Therefore, when a perfect square that is not divisible by 6 is divided by 6, the possible remainders are 1, 3, or 4.

### Final Answer:
The remainder when a perfect square, not divisible by 6, is divided by 6 can be 1, 3, or 4.