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Vedic Division
Here, you will learn the Nikhilam Method of Division.
Lets start with a simple sum. 1. 1853 ÷ 8
Step 1: Separate the dividend (1853) into two parts such that the right hand side of the dividend would contain as many digits as the divisor (8, which is 1 digit). Here, the dividend is divided into 185/3. Name 185 as A and 3 as B.
Step 2: Find complement of the divisor. The divisor is 8 and 8 comes in base 10, so its compliment is 2. Write the complement below 8 and name it C.
Step 3: Write the first digit of the dividend (1) as it is.
Step 4: Multiply the digit which you wrote below in Step 3 and multiply it with C. (1 * 2) gives us 2 here. Now, write it below the next number in the dividend i.e 8 and add themto get 10. write down 10 beside the (1) which you carried down as it is, separated by | .
Step 5: Now multiply the (10) which you wrote down just now with C to get 10*2 which is 20. write it below the next digit of our dividend (5) and add them to get 25. Write it beside 1 | 10 to get 1 | 10 | 25.
Step 6: Similarly to step 5, multiply (25) with C to get 50. Write it below the next digit of the dividend (3), which also happens to be the last. Add them to get 53 and write it beside 1 | 10 | 25. You now have 1 | 10 | 25 | 53. Keep on doing this till you do this with every digit of the dividend. We will stop here because we already did it here.
Step 7: Separate the last term from 1 | 10 | 25 | 53. This will be our remainder. The other part is the quotient. 1 | 10 | 25 || 53. The green part will be the remainder and the red part will be the quotient after using balancing rule. However, 53 cannot be the remainder in 1853 ÷ 8 because it is higher than 8. Therefore, we will divide 53 by 8 to get quotient as 6 and remainder 5. Now, add the quotient to the previous quotient to get 1 | 10 | 25 + 6 || 5
= 1 | 10 | 31 || 5
Now, use balancing rule on 1 | 10 | 31 to get 231 as the actual quotient.
Quotient = 231, Remainder = 5.
2. 1231 ÷ 7
After doing the procedure from Step 1 to Step 6, we get this.
55 is the remainder we have, and by dividing it by 7 we get 7 as quotient and 6 as remainder. now we have 1 | 5 | 25 || 6
Quotient = 175, Remainder = 6
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