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You are here: Home / What is Vedic Mathematics / Multiplication in Vedic Mathematics / Nikhilam Sutra – Shortcut To Multiply Numbers in Vedic Mathematics

Nikhilam Sutra – Shortcut To Multiply Numbers in Vedic Mathematics

February 6, 2013 by Rahul Bhangale 14 Comments

Vedic Mathematics Nikhilam Sutra

Nikhilam Navatascaramam Dastah (Nikhilam Sutra)

Shortcut method of multiplication using Vedic Mathematics when numbers are closer to power of 10 (10,100,1000,…)

Sanskrit Name:

        निखिलं नवतस्चरमं दशतः

English Translation:

All from 9 and last from 10.

Stuff you need to know before starting:

Before starting with Nikhilam Sutra Multiplication, I recommend you to go through the 2.Vinculum Process. (Vinculum Process will be used in Type 3 of Nikhilam Tecnique)

Specific Condition Required:

Numbers need to be close* to power of 10 (10, 100, 1000, etc).

Also Read => More Vedic Mathematics Sutras for Multiplication.

Process:

  1. Depending upon the numbers closer to power of 10, we select that power of 10 as our Base.
  2. Apply the principle of Nikhilam i.e. subtract the digits from Base – All the digits from 9 and last from 10.  (write besides those numbers) (See below example 94 * 96). Those numbers if positive will be called as exceses and if negative will be called as deficiencies.
  3. Multiply those deficiencies or excesses. (write in 2nd compartment).
  4. Do Cross Addition of Numbers with deficiencies or excesses. (write in 1st Compartment)
  5. 2nd compartment ALWAYS needs to have same number of digits as that of zeroes of the selected Base. If less then pre-append zeroes. If more, carry forward initial digits to 1st compartment
  6.  Below Examples will clear the process. Nikhilam Sutra can be classified in 3 groups as follows:

Nikhilam Type 1:

This type of Nikhilam Sutra can be applied when numbers slightly* less than power of 10 (10, 100, 1000, etc.).

Formula used: (x-a)(x-b) = x(x-a-b) + ab

Vedic Mathematics- Shortcut Method to multiply numbers when numbers are closer to power of 10

Shortcut Method in Vedic Mathematics to multiply numbers when numbers are closer to power of 10

 Nikhilam Type 2:

Numbers slightly* greater than power of 10 (10, 100, 1000, etc.).

Formula used:(x+a)(x+b) = x(x+a+b) + ab

Vedic Mathematics- Shortcut Method to multiply numbers when numbers are closer to power of 10

Vedic Mathematics- Trick to multiply numbers when numbers are closer to power of 10

 Nikhilam Type 3:

Numbers closer to* & present on either side of power of 10 (10, 100, 1000, etc.). This type of Nikhilam will require understanding of 2.Vinculum Process.

Formulas used:

  • (x+a)(x-b) = x(x+a-b) – ab
  • (x-a)(x+b) = x(x-a+b) – ab

Vedic Mathematics- Shortcut Method for multiplication of numbers when numbers are closer to power of 10

Vedic Mathematics- Trick to multiply numbers when numbers are closer to power of 10

Also Read => How to divide numbers using Nikhilam Sutra in Vedic Mathematics.

Nikhilam Multiplication Tips (*):

If we observe above multiplication of 998 and 1123, even though numbers are NOT very close to power of 10 but still we can easily manage to apply Nikhilam Method. This is because we ALSO have to take consideration of multiplication of excessive/deficiency with the number. If multiplication of them is easily manageable then we can apply Nikhilam Method.

Restating Specific Condition Required (*):

Numbers need NOT to be close to power of 10 BUT multiplication of excess/deficiency with the numbers should be manageable. But if numbers are closer to power of 10 then we can surely apply any of the Nikhilam Method.

What You Think ????

Which of the following examples should be solved using Nikhilam Sutra and which should not be and why ?? (Lets see how many of you understood the Nikhilam Sutra:))

  1. 87 x 108
  2. 1112 x 1003
  3. 1112 x 1108
  4. 56 x 98
  5. 56 x 53
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Comments

  1. Ann says

    November 16, 2015 at 8:00 AM

    Hi Rahul.

    I tried multiplying 1006*999 (type 3). I get the answer 1005006 using this method ; but the correct answer is 1004994. Could you please let me know where I went wrong?

    Log in to Reply
    • Rahul Bhangale says

      November 17, 2015 at 3:56 AM

      Hello Ann,

      You must have got 1005/Bar(006). This is a Vinculum Number and hence needs to be converted to Normal Number.
      I recommend to check Type 3 examples which similarly has Vinculum number and check videos for converting vinculum number to normal number
      https://youtu.be/f88ya7GeoeI
      https://youtu.be/9Fm8VCRr_i0

      Conversion of Vinculum Number (1005Bar(006)) will give 1004994.

      Log in to Reply
      • Ann says

        November 17, 2015 at 6:24 AM

        Hi Rahul,

        Yes I got it now, thanks.

        Log in to Reply
  2. Snehi poddar says

    August 12, 2014 at 5:45 PM

    Sir if we have to multiply 1007 * 56 ..
    By nikilum method. The base of 1007 is 1000 and base of 56 is 100 ..
    then how to multiply in this situation.?

    Log in to Reply
    • Rahul Bhangale says

      August 23, 2014 at 6:17 AM

      Hello Snehi,

      Each technique in Vedic Mathematics is based on what type of number we have.

      As mentioned in Specific Condition “Numbers need NOT to be close to power of 10 BUT multiplication of excess/deficiency with the numbers should be manageable.”

      Both numbers should have same base and needs to be closer so that multiplication of excess/deficiency with the numbers is manageable.

      For such problems use general multiplication rule: Urdhva Tiryak Sutra.
      http://mathlearners.com/vedic-mathematics/multiplication-in-vedic-mathematics/urdhva-tiryak/

      Log in to Reply
  3. Amit Shukla says

    May 16, 2014 at 2:15 PM

    what is mean of multiplication of deficiencies or excess should be “manageble”…?

    Log in to Reply
    • Rahul Bhangale says

      June 10, 2014 at 3:12 AM

      Using Nikhilam Sutra it is possible to multiply numbers like 98 and 32 even though 32 is not closer to power of 10. But it is difficult to multiply 32 and 56.

      Please check the mentioned Nikhilam Multiplication Tips (*).

      Log in to Reply
  4. AJINKYA says

    February 24, 2014 at 7:18 AM

    87*108

    87/-13
    108/=O8
    ———-
    —
    95/104
    MY ANS IS 10396
    BUT IT SHOULD BE 9396
    PLEASE EXPLAIN.
    GR8 SITE!!! THANKS

    Log in to Reply
    • AJINKYA says

      February 24, 2014 at 7:33 AM

      SORRY GOT MY ANS 3 TYPE.THANKS

      Log in to Reply
      • Rahul Bhangale says

        February 24, 2014 at 12:48 PM

        Yup Ajinkya … thats right its Type 3 multiplication.

        Keep learning Vedic Mathematics !!!

        Log in to Reply
  5. yogini says

    July 25, 2013 at 9:38 AM

    the multiplication of 1007*988 is either wrong or i m doind sumthing wrong,please guide me
    my answer always comes 99416
    but the actual multiplicatin of these 2 numbers is 994916

    please help me
    988 -12
    1007 +7
    ———
    995 | -84
    ———
    –>99416
    what mistake i must be making

    Log in to Reply
    • yogini says

      July 25, 2013 at 9:39 AM

      okay got my mistake no problem
      it must be 084 instead of just 84 isnt it

      how dare i question vedic math :)
      problem solved

      Log in to Reply
      • Rahul Bhangale says

        August 3, 2013 at 5:53 PM

        Yes, thats correct Yogini…right hand side should be 084 as the numbers are closer to 1000 (base=1000).

        Log in to Reply
    • Deepak Trivedi says

      October 11, 2013 at 11:34 AM

      988 -12
      1007 +7
      ———
      995 | -84
      ———
      –>99416

      You have done mistake 995| -084
      994|1000-084
      994|916
      Ans

      Log in to Reply

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