Subjects arithmetic

Vedic Division 3367A9

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1. **State the problem:** Find the quotient and remainder when 67802 is divided by 34 using the Vedic division method. 2. **Formula and rules:** Vedic division uses a method of successive approximation and adjustment to find quotient and remainder without long division. 3. **Step 1:** Estimate quotient by dividing the leading digits. Here, 67802 รท 34. 4. **Step 2:** Approximate quotient: $\frac{67802}{34} \approx 1994$ (since $34 \times 2000 = 68000$ which is slightly more than 67802). 5. **Step 3:** Multiply quotient estimate by divisor: $1994 \times 34 = 1994 \times (30 + 4) = 1994 \times 30 + 1994 \times 4 = 59820 + 7976 = 67796$. 6. **Step 4:** Subtract this product from the dividend to find remainder: $67802 - 67796 = 6$. 7. **Step 5:** Since remainder 6 is less than divisor 34, the quotient is correct. **Final answer:** Quotient = 1994, Remainder = 6.