To convert the number 876 from base-10 to base-6, follow these steps:
1. Initial Division and Remainder:
- Divide 876 by 6.
- The quotient is 146 and the remainder is 0.
- Write down the remainder (0). This is the least significant digit in the base-6 number.
2. Next Division:
- Take the quotient from the previous division (146) and divide it by 6.
- The new quotient is 24 and the new remainder is 2.
- Write down this remainder (2) to the left of the previous remainder.
3. Continue the Process:
- Take the quotient from the previous step (24) and divide it by 6.
- The new quotient is 4 and the new remainder is 0.
- Write down this remainder (0) to the left of the previous digits.
4. Final Division:
- Take the quotient from the previous step (4) and divide it by 6.
- The new quotient is 0 (since 4 divided by 6 is less than 1) and the remainder is 4.
- Write down this remainder (4).
Now, you have written down all the remainders from the divisions starting from the least significant digit (rightmost) to the most significant digit (leftmost). The remainders in reverse order give us the number in base-6.
Putting it all together, the digits you wrote down from least significant to most significant are: 0, 2, 0, 4.
Thus, the base-6 representation of the base-10 number 876 is:
4020
So, the base-6 number is 4020.
