Finding Remainders
Shortcuts to find remainders without dividing.
Core Concepts
Often we only need to know the Remainder (what is left over), not the full quotient. Vedic Math gives us super-fast rules for this!
Key Rules
- By 9: Sum of digits. (e.g., 12 ÷ 9 -> 1+2=3).
- By 3: Sum of digits.
- By 11: Alternating sum (Right to Left: + - + -).
- By 2: Last digit (Even=0, Odd=1).
- By 5: Last digit (0 or 5 -> 0).
- By 4: Last 2 digits.
Solved Examples
Example 1: Remainder by 9
Question: Find remainder of 1234 ÷ 9.
• Sum: 1 + 2 + 3 + 4 = 10.
• Reduce: 1 + 0 = 1.
• Answer: 1.
Example 2: Remainder by 11
Question: Find remainder of 273 ÷ 11.
• Alt Sum (Right to Left): 3 - 7 + 2.
• Calculate: 3 - 7 = -4. -4 + 2 = -2.
• Adjust: Since result is negative, add 11. -2 + 11 = 9.
• Answer: 9.
Example 3: Remainder by 4
Question: Find remainder of 1923 ÷ 4.
• Rule: Check last 2 digits.
• Last 2: 23.
• Divide: 23 ÷ 4 = 5 with Remainder 3.
• Answer: 3.
Example 4: Remainder by 5
Question: Find remainder of 487 ÷ 5.
• Rule: Check last digit.
• Last digit: 7.
• Divide: 7 ÷ 5 = 1 with Remainder 2.
• Answer: 2.
