Multiplication of two digit number greater than base (13 x 16, 17 x 18)


Multiplication of two-digit numbers

In Vedic Maths, Multiplication of two digit numbers can be done by Nikhilam Sutra (Base Method)
Case 1: -  Both Numbers are higher than Base (10)

For Example:- 13 x 16
Step 1 –

Number Base Difference
13 (X1) 10 (Y) + 3 (Z1)
16 (X2) 10 (Y) + 6 (Z2)

Y= nearest power of 10 i.e. 10, 100, 1000, 10000. 
Thus nearest power of 10 to the number 13 and 16 is 10.

1 = X – Y, Z 2 = X 2 - Y

Step 2 -

Part A Part B
13 + 6 3 x 6
19 18

Part A = (X1 + Z 2)
Part B = Z1 x Z2

Step 3 - 

Part A Part B
19 + 1 8
20 8

Ans :- 208

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

 

 Another Example of Two Digit Numbers higher than Base (10)
17 x 18

Step 1 –

Number Base Difference
17 (X1) 10 (Y)  + 7 (Z1)
18 (X2) 10 (Y)  + 8 (Z2)

Y= nearest power of 10 i.e 10, 100, 1000, 10000. 
Thus nearest power of 10 to the number 17 and 18 is 10.
Z 1 = X 1 – Y , Z 2 = X 2 - Y

Step 2: -

Part A Part B
17 + 8 7 x 8
25 56

Part A = (X1 + Z2)
Part B = (Z1 x Z2)

Step 3 :- 

Part A Part B
25 +5 6
30 6

Ans :- 306

Rule 1:- No. of zeros in base is equal to no. of digits in part B. 
Therefore 5 carried over to Part A
Now Club Part A with Part B for Final Answer.

time: 0.0102000237