To convert $59$ from base 10 to base 6:

1. Start by dividing $59$ by $6$ to determine the quotient and remainder:

   • $59 \div 6 = 9$ remainder $5$.

   So, the least significant digit (rightmost) in base 6 is $5$.

2. Take the quotient ($9$) and divide it by $6$:

   • $9 \div 6 = 1$ remainder $3$.

   This means the next digit is $3$.

3. Finally, take the quotient ($1$) and divide it by $6$:

   • $1 \div 6 = 0$ remainder $1$.

   This gives the most significant digit (leftmost) as $1$.

Putting it together from most significant to least significant, $59_{10} = 135_6$.

Would you like additional steps or further explanation?

Here are 5 related questions you might explore:

1. How do you convert a number from base 6 to base 10?
2. What are the general rules for converting between different bases?
3. How would you represent other numbers like $75$ in base 6?
4. Why is base 6 used in certain numeral systems?
5. Can you explain the difference between positional notation in different bases?

Tip: Always remember to read remainders from last to first to form the correct base number.