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:
 Depending upon the numbers closer to power of 10, we select that power of 10 as our Base.
 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.
 Multiply those deficiencies or excesses. (write in 2nd compartment).
 Do Cross Addition of Numbers with deficiencies or excesses. (write in 1st Compartment)
 2nd compartment ALWAYS needs to have same number of digits as that of zeroes of the selected Base. If less then preappend zeroes. If more, carry forward initial digits to 1st compartment
 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: (xa)(xb) = x(xab) + ab
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
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)(xb) = x(x+ab) – ab
 (xa)(x+b) = x(xa+b) – ab
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:))

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Ann says
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?
Rahul Bhangale says
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.
Ann says
Hi Rahul,
Yes I got it now, thanks.
Snehi poddar says
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.?
Rahul Bhangale says
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/vedicmathematics/multiplicationinvedicmathematics/urdhvatiryak/
Amit Shukla says
what is mean of multiplication of deficiencies or excess should be “manageble”…?
Rahul Bhangale says
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 (*).
AJINKYA says
87*108
87/13
108/=O8
———
—
95/104
MY ANS IS 10396
BUT IT SHOULD BE 9396
PLEASE EXPLAIN.
GR8 SITE!!! THANKS
AJINKYA says
SORRY GOT MY ANS 3 TYPE.THANKS
Rahul Bhangale says
Yup Ajinkya … thats right its Type 3 multiplication.
Keep learning Vedic Mathematics !!!
yogini says
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
yogini says
okay got my mistake no problem
it must be 084 instead of just 84 isnt it
how dare i question vedic math
problem solved
Rahul Bhangale says
Yes, thats correct Yogini…right hand side should be 084 as the numbers are closer to 1000 (base=1000).
Deepak Trivedi says
988 12
1007 +7
———
995  84
———
–>99416
You have done mistake 995 084
9941000084
994916
Ans