Multiply any number with 111

 

In the tutorial, we learnt the shortcut,  how to multiply any number with 11.  In this tutorial on Mathematical shortcut, we will learn how to multiply any number with 111. The same technique can be used to multiply any number with a sequence of 1’s like 11, 111, 1111 and so on.

How to multiply any number with 111


Let me explain with a simple example. Let’s say we want to multiply the number 345 x 111.

Let’s understand the steps involved.

 

multiplication_111_1

 

Step 1 :  First step, remains the same. We write the right most digit i.e., 5 as it is.

Step 2 :  Next we start from the right and take the last 2-digits, 4 and 5 and add them and write 9.

Step 3 :  Now, this is important and different from the previous tutorial. In the tutorial on how to multiply any number with 11, we used to take 2 numbers at a time.  Whereas here, we take 3 digits at a time.  This is because, we are multiplying with 111 (series of 3 1’s). So we need to add the digits, 3, 4 and 5 which gives us 12. So we write 2 and carry forward 1.  This step is continued till we no-longer have 3 digits to add.

Step 4 :  Since we donot have any more digits to add, we will add the first 2-digits 3 and 4 which gives us 7. Add the carry-forward 1 from the previous addition. So we write 8.

Step 5 :  This is the last step. We write the left most digit i.e., 3 as it is the only digit left.

So, Can you compute what is 3805 x 111 ?

 

multiplication_111_3

Very easy right 🙂

Can you compute what is 12345 x 111 ?

 

multiply_111_2

So, no matter how big the number is, the important thing is whenever, you are multiplying a number with 111, you take 3-digits at a time and add them.

Let’s take another example now.

 

Can you try multiplying 45 x 111?


Notice that the number of digits in the number is 2( less the number of digits in 111). In order that this shortcut works, the minimum number of digits should be same as in 111. So, we append a 0 in 45 before we using this shortcut.

 

multiply_111_3

 

On the similar lines, can you multiply ?

  • 8585 x 111
  • 759 x 111
  • 909 x 111
  • 1234589 x 111


Please leave a comment or contact me, if you any doubts related to this tutorial. 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.

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