LikhoPadho

Multiplication of three-digit numbers

In Vedic Maths, Multiplication of three digit numbers can be done by Nikhilam Sutra (Base Method)
Case 1: -  Both Numbers are greater than Base (100)

For Example:- 105 x 108
Step 1 –

Number	Base	Difference
105 (X1)	100 (Y)	+ 5 (Z1)
108 (X2)	100 (Y)	+ 8 (Z2)

Y= nearest power of 10 i.e. 10, 100, 1000, 10000. 
Thus nearest power of 10 to the number 105 and 108 is 100.
Z 1 = X 1 – Y, Z 2 = X 2 - Y

Step 2 -

Part A	Part B
105 + 8	5 x 8
113	40

Part A = (X1 + Z 2)
Part B = Z1 x Z2

Step 3 - 

Part A	Part B
113	40

Ans :- 11340

Rule 1:- No. of zeros in base is equal to no. of digits in part B. 
Therefore here no. of zeros in base is equal to no. of digits in part B 
Now Club Part A with Part B for Final Answer
 

Another Example of Three Digit Numbers greater than Base (100)

107 x 112

Step 1 –

Number	Base	Difference
107 (X1)	100 (Y)	+ 7 (Z1)
112 (X2)	100 (Y)	+ 12 (Z2)

Y= nearest power of 10 i.e 10, 100, 1000, 10000. 
Thus nearest power of 10 to the number 107 and 112 is 100.
Z 1 = X 1 – Y, Z 2 = X 2 - Y

Step 2 -

Part A	Part B
107 + 12	7 x 12
119	84

Part A = (X1 + Z 2)
Part B = Z1 x Z2

Step 3 - 

Part A	Part B
119	84

Ans :- 11984

Rule 1:- No. of zeros in base is equal to no. of digits in part B.
Therefore here no. of zeros in base is equal to no. of digits in part B 
Now Club Part A with Part B for Final Answer