Divide 34211 by 3: Step-by-Step Long Division Problem

To solve the problem, we will perform long division of 34211 by 3:

• Step 1: Divide the first digit of 34211, which is 3, by 3. $3 \div 3 = 1$. Write 1 on top.
• Step 2: Subtract $1 \times 3 = 3$ from the first 3, getting a remainder of 0. Now bring down the next digit, 4, making it 04.
• Step 3: Divide 04 by 3. $4 \div 3 = 1$. Write 1 on top.
• Step 4: Subtract $1 \times 3 = 3$ from 4, getting a remainder of 1. Bring down the next digit, 2, making it 12.
• Step 5: Divide 12 by 3. $12 \div 3 = 4$. Write 4 on top.
• Step 6: Subtract $4 \times 3 = 12$ from 12, getting a remainder of 0. Bring down the next digit, 1, making it 01.
• Step 7: Divide 01 by 3. $1 \div 3 = 0$. Write 0 on top.
• Step 8: Subtract $0 \times 3 = 0$ from 1, getting a remainder of 1. Bring down the final digit, 1, making it 11.
• Step 9: Divide 11 by 3. $11 \div 3 = 3$. Write 3 on top.
• Step 10: Subtract $3 \times 3 = 9$ from 11 to get a remainder of 2.

After completing the division, the quotient is $11403$ and the remainder is $2$.

Therefore, the solution to the problem is $\mathbf{11403}$ with a remainder of $\mathbf{2}$.