# Multiply any 3 digit numbers

In the previous tutorial on multiplication of any 2-digit number, we learnt how to multiply any 2-digit numbers  using criss-cross method of multiplication.

In this tutorial,  we will understand a very important mathematical shortcut of multiplying any two 3 digit numbers using the criss-cross multiplication technique.

For students preparing for competitive examination, You might come across, many multiplications in the competitive examinations where you might be asked to multiply two 3-digit number.

If you know criss-cross method, you can save a lot of time by eliminating the choices at the end of each step of criss-cross multiplication.
The number of steps in a 3 x 3 multiplication is 5. Let’s understand the steps with an example.

Example : Suppose you want to multiply 132 x 214.

Step 1 :   Write the numbers one below the other. Multiply the digits in the unit place as in 2×2 multiplication, that is 2×4=2. This will be the unit digit of the answer as well. Step 2 :
Now, cross multiply the digits in the 10’s and unit’s place to get the digit in the 10’s place of the answer. Step 3 :
Now, notice the criss-cross multiplication.  Here, we multiply the terms (1×4), (2×2) and (3×1) and then add these terms to get 11. Step 4 :
Now, repeat Step 2 with the digits in the 100’s and the 10’s place. Step 5 :
This is the last step in the multiplication. Now, repeat Step 1 with the digits in 100’s place. The complete steps involved in the calculation is illustrated in the figure : Notice the carry-forward in each step.

On the similar lines, can you multiply,

• 423 x 234
• 124 x 465
• 567 x 890
• 646 x 772

Easy ?

I hope this tutorial is useful. If you have any doubts concerning this tutorial, please leave a comment, I would be glad to help. ### Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

1. Santanu Mahadani

There are some misspell….step III and V

• Kiran Chandrashekhar

Thanks so much Santanu for pointing it out. I have corrected it 🙂
Kiran

2. Sakuriu

Great tutorial…very helpfull : )
There is a miscalculation in step III, the result should be 11 instead of 14

• Kiran Chandrashekhar

Thank you so much for pointing it out. I am extremely sorry for the inadvertent error though.
I am glad you liked it.

Thanks
Kiran

3. ramya

sir pls solve that multiply numbers 68*73

ur steps are:
1st step:
8*3=27
2nd Step:
(6*3)+(7*8)
18+56=74
3rd Step:
6*7= 42

therefore, 42/74/27

and written off 42/4/7
7 2
then 4987 this anwer is wrong sir .
pls give me detailed soultion ur reply im waited

• Kiran Chandrashekhar

Hello Ramya,

Here are the steps :

68*73 = 6*7 / (6*3 + 8*7) / 8*3
= 42/74/24
=4964

4. sourav lala

the vth step should be 2 and not 8.
anyway thanks for such an eloquent explanation.

5. jamesn

This is very useful technique , I wished it was taught to me in school