How to remember multiplication tables having same digits



I found it so difficult myself. Growing up as a student, I was really poor at memorizing number. Now, I know, I was not alone. One of the things students find hard is to memorize tables. I would say, we should never memorize the multiplication tables. When you start memorizing, you fail to observe the patterns in the multiplication. This tutorial is on a series of tutorials on how to remember multiplication tables.

In this tutorial, we will see how to remember the tables having same digits like 11, 22, 33. Later, we will see how to remember the tables of digits having the same digits like 2222, 4444, 9999 and so on.

Multiplication Table of 2-digit number where digits are same


Let us understand with a very simple example. Let us say, we want to remember the multiplication table of 55.

Step 1 : Write the multiplication table of 5. You already know this. I am just repeating it here.

Product Multiplication
5 x 1 05
5 x 2 10
5 x 3 15
5 x 4 20
5 x 5 25
5 x 6 30
5 x 7 35
5 x 8 40
5 x 9 45
5 x 10 50

Step 2 : Now the multiplication table of 55 can be easily obtained by looking at the multiplication table of 5.

Just separate the digits in the 5 multiplication table. The middle digit is obtained by adding the first and the last digit as shown in the multiplication table.

Product 5 Tables 55 Tables 55 Tables
55 x 1 0 __ 5 0 (0+5) 5 055
55 x 2 1 __ 0 1 (1+0) 5 110
55 x 3 1 __ 5 1 (1+5) 5 165
55 x 4 2 __ 0 2 (2+0) 0 220
55 x 5 2 __ 5 2 (2+5) 5 275
55 x 6 3 __ 0 3 (3+0) 0 330
55 x 7 3 __ 5 3 (3+5) 5 385
55 x 8 4 __ 0 4 (4+0) 0 440
55 x 9 4 __ 5 4 (4+5) 5 495
55 x 10 5 __ 0 5 (5+0) 0 550

This is pretty cool right 🙂

Can you then right the multiplication table of 77 ?

Product 7 Tables 77 Tables 77 Tables
77 x 1 0 __ 7 0 (0+7) 7 077
77 x 2 1 __ 4 1 (1+4) 4 154
77 x 3 2 __ 1 2 (2+1) 1 231
77 x 4 2 __ 8 2 (2+8) 8 308
77 x 5 3 __ 5 3 (3+5) 5 385
77 x 6 4 __ 2 4 (4+2) 2 462
77 x 7 4 __ 9 4 (4+9) 9 539
77 x 8 5 __ 6 5 (5+6) 6 616
77 x 9 6 __ 3 6 (6+3) 3 693
77 x 10 7 __ 0 7 (7+0) 0 770

Important : When the addition results in a number which is greater than 10, it is carry forward just like in multiplication.

For instance, consider 77 x 8 :

 

 

Multiplication Table of 3 or more digit number where digits are same

Let us see, how to remember the multiplication tables of numbers having the same digits like 2222, 4444, 9999 and so on.

When you are obtaining the multiplication table of 555, you repeat the middle digit (obtained by taking the sum of the digits of multiplication table 5) twice. Similarly, when you are obtaining the multiplication table of 5555, you repeat it thrice and so on.

The multiplication table of 555, 5555 is given in the below table.

Product 5 Tables 55 Tables 555 Tables 5555 Tables
55 x 1 0 __ 5 055 0 (55) 5 = 555 0 (555) 5 = 5555
55 x 2 1 __ 0 110 1 (11) 0 = 1110 1 (111) 0 = 11110
55 x 3 1 __ 5 165 1 (66) 5 = 1665 1 (666) 5 = 16665
55 x 4 2 __ 0 220 2 (22) 0 = 2220 2 (222) 0 = 22220
55 x 5 2 __ 5 275 2 (77) 5 = 2775 2 (777) 5 = 27775
55 x 6 3 __ 0 330 3 (33) 0 = 3330 3 (333) 0 = 33330
55 x 7 3 __ 5 385 3 (88) 5 = 3885 3 (888) 5 = 38885
55 x 8 4 __ 0 440 4 (44) 0 = 4440 4 (444) 0 = 44440
55 x 9 4 __ 5 495 4 (99) 5 = 4995 4 (999) 5 = 49995
55 x 10 5 __ 0 550 5 (55) 0 = 5550 5 (555) 0 = 55550

 

Now, let us consider the multiplication of 777, 7777 and so on.

There is a slight variation here. When we were obtaining the multiplication table of 777, 7777 and so on, the addition of the digits results in a carry. This additional carry is forwarded to all the digits on the left

For instance, consider 7777 x 8 :

 


The multiplication table of 777, 7777 is given in the below table.

Product 7 Tables 77 Tables 777 Tables 7777 Tables
77 x 1 0 __ 7 077 0 (77) 7 = 777 0 (777) 7 = 7777
77 x 2 1 __ 4 154 1 (55) 4 = 1554 1 (555) 4 = 15554
77 x 3 2 __ 1 231 2 (33) 1 = 2331 2 (333) 1 = 23331
77 x 4 2 __ 8 308 2 (00) 8 = 3108 2 (000) 8 = 31108
77 x 5 3 __ 5 385 3 (88) 5 = 3885 3 (888) 5 = 38885
77 x 6 4 __ 2 462 4 (66) 2 = 4662 4 (666) 2 = 46662
77 x 7 4 __ 9 539 4 (33) 9 = 5439 4 (333) 9 = 54439
77 x 8 5 __ 6 616 5 (11) 6 = 6216 5 (1111) 6 = 62216
77 x 9 6 __ 3 693 6 (99) 3 = 6993 6 (9999) 3 = 69993
77 x 10 7 __ 0 770 7 (77) 0 = 7770 7 (7777) 0 = 77770


If you know the multiplication table of 2, 3,4 and so on, you can now remember the multiplication table like 111, 222, 33333, 55555 and so on without memorizing anything.

I hope you find the tutorial very useful. Please leave a comment or contact me, if you have any doubts or any comments on this topic. I would be glad to answer.

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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