The denary number 43125 in the scale of 6 will be represented by

Options

A. 353135
B. 531353
C. 515313
D. 55453

Answer

To convert the denary number 43125 into base 6, we will follow these steps:

### Step-by-Step Solution:

1. **Divide the Number by 6**: Start with the number 43125 and divide it by 6.
\[ 43125 \div 6 = 7187 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 43125 - (6 \times 7187) = 3 \]

2. **Record the Remainder**: The remainder from the first division is 3. This will be the least significant digit (rightmost) in the base 6 representation.

3. **Repeat the Division**: Now take the quotient (7187) and divide it by 6.
\[ 7187 \div 6 = 1197 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 7187 - (6 \times 1197) = 5 \]

4. **Record the Remainder**: The remainder from this division is 5. This will be the next digit in the base 6 representation.

5. **Continue Dividing**: Take the new quotient (1197) and divide it by 6.
\[ 1197 \div 6 = 199 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 1197 - (6 \times 199) = 3 \]

6. **Record the Remainder**: The remainder is 3. This will be the next digit in the base 6 representation.

7. **Repeat Again**: Take the quotient (199) and divide it by 6.
\[ 199 \div 6 = 33 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 199 - (6 \times 33) = 1 \]

8. **Record the Remainder**: The remainder is 1. This will be the next digit in the base 6 representation.

9. **Final Division**: Take the quotient (33) and divide it by 6.
\[ 33 \div 6 = 5 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 33 - (6 \times 5) = 3 \]

10. **Record the Remainder**: The remainder is 3. This will be the next digit in the base 6 representation.

11. **Last Division**: Finally, take the quotient (5) and divide it by 6.
\[ 5 \div 6 = 0 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 5 \]

12. **Record the Remainder**: The remainder is 5. This will be the most significant digit (leftmost) in the base 6 representation.

### Compile the Digits:
Now, we compile the remainders from the last to the first:
- Most significant to least significant: 5, 3, 1, 3, 5, 3

Thus, the representation of the denary number 43125 in base 6 is:
\[ \text{43125}_{10} = 531353_{6} \]

### Final Answer:
The denary number 43125 in the scale of 6 will be represented by \( 531353_{6} \).