# Column Method of Multiplication

We will discuss here about the column method of multiplication. We know how to multiply a 2-digit number by a 1-digit number and 2-digit number. We also know how to multiply a 3-digit number by a 1-digit number. Similarly, we can multiply a 2-digit number by a 2-digit number.

Example: Multiply 84 by 36.

Solution:

Here multiplicand is 84 and multiplier is 36

Step I: Multiply multiplicand by the ones digit of multiplier i.e.,

2

8              4

×             6 ones

5              0              4 ones  partial product

Step II: Multiply multiplicand by the tens digit of multiplier i.e.,

1

8              4

×             3 tens

2              5              2 tens partial product

504 ones + 252 tens

504 × 1 + 252 × 10

504 + 2520 = 3024

It actually means.

8              4

×             3              3

5              0              4                               84 × 6 = 504

2              5              2              0                        84 × 30 = 2520

3              0              2              4                        84 × 36 = 3024

Now we shall apply the same method to multiply a 3-digit number by a 2-digit number.

1              5              3

×             2              4

6              1              2        153 × 4   = 612    partial product

3              0              6              0        153 × 20 = 3060  partial product

3              6              7              2        153 × 24 = 3672

Shortcut method (3-digit number by a 2-digit number) → Without Regrouping

Step I:

1              2              3

×             1              2

6

Step II:

1              2              3

×             1              2

4              6

Step III:

1              2              3

×             1              2

2              4              6

Step IV:

1              2              3

×             1              2

2              4              6

3              ×

7              6

Step V:

1              2              3

×             1              2

2              4              6

2              3              ×

4              7              6

Step VI:

1              2              3

×             1              2

2              4              6

1              2              3              ×

1              4              7              6