Complement Division
The Nikhilam Method for Division.
Core Concepts
Just like we used the Base Method for multiplication, we can use it for division too! This method is perfect when dividing by numbers close to a base (like 8, 9, 98, 99).
The Method
1. Find the Complement: How much is the divisor below the Base? (e.g., for 8, base is 10, complement is 2).
2. Split the Dividend: Separate the last digit(s) for the Remainder (same number of zeros in base).
3. Multiply and Add: Bring down the first digit, multiply by the complement, and add to the next column.
Solved Examples
Example 1: 12 ÷ 8
Question: Solve 12 ÷ 8.
• Base: 10. Complement: 2 (since 10-8=2).
• Split: 1 | 2 (One digit for remainder).
• Step 1: Bring down 1.
• Step 2: Multiply 1 × 2 = 2. Add to next column: 2 + 2 = 4.
• Answer: Q: 1, R: 4.
Example 2: 23 ÷ 9
Question: Solve 23 ÷ 9.
• Base: 10. Complement: 1.
• Split: 2 | 3.
• Step 1: Bring down 2.
• Step 2: Multiply 2 × 1 = 2. Add to next column: 3 + 2 = 5.
• Answer: Q: 2, R: 5.
Example 3: 111 ÷ 8
Question: Solve 111 ÷ 8.
• Base: 10. Complement: 2.
• Split: 11 | 1.
• Step 1: Bring down 1.
• Step 2: 1 × 2 = 2. Add to next column: 1 + 2 = 3.
• Step 3: 3 × 2 = 6. Add to remainder column: 1 + 6 = 7.
• Answer: Q: 13, R: 7.
Example 4: Base 100 (104 ÷ 98)
Question: Solve 104 ÷ 98.
• Base: 100. Complement: 02.
• Split: 1 | 04 (Two digits for remainder).
• Step 1: Bring down 1.
• Step 2: 1 × 02 = 02. Add to 04: 04 + 02 = 06.
• Answer: Q: 1, R: 6.
