Math Trick 4: A Shortcut on Multiplying Numbers by 13

This is the fourth part of the Math and Multimedia’s Math Tricks and Shortcuts Series. In this post, I am going to discuss a shortcut on multiplying numbers by 13 (my aplogies to all the triskaidekaphobic). Well, I am not really sure if you would like to call it a shortcut since multiplying large numbers by 13 using the conventional method might be faster. Anyway, I am going to show you though that it works with few cases and we will later discuss why it works.

Shortcut on Multiplying Numbers by 13

Append 0 before and after the number you are multiplying by 13.

Starting with the ones digit of the original number, multiply it by 3 and add the product to the next digit on the right.  The result of this calculation is the ones digit of the product of the number and 13.

Do the process again to the tens digit. Multiply it by 3 and add the product to the next digit on the right. The result of the calculation is the tens digit of the product of the number and 13.

Do this to each of the remaining digits from right to left and place the result of the calculation in appropriate place value of the product. If the sum exceed by 10, carry over the tens digit and add to the next result.

Example 1: 221 x 13

Append 0 before and after the number you are multiplying by 13: 02210

Starting with the ones digit of the original number, multiply it by 3 and add the product to the next digit on the right.  The result is the ones digit of the product of the number and 13.

Calculation: 1 x 3 + 0 = 3

Do this also to the tens digit. The result of the calculation is the tens digit of the product of the number and 13.

Calculation: 2 x 3 + 1 = 7

Do this to each digit of the remaining digits from right to left.

Calculations:

2 x 3 + 2 = 8

0 x 3 + 2 = 2

So, 221 x 13 = 2873

 

Example 2: 5301 x 13

Append 0 before and after: 053010

Calculation:

1 x 3 + 0 = 3 (take 3 as ones digit of the product)

0 x 3 + 1 = 1 (take 1 tens digit of the product)

3 x 3 + 0 = 9 (take 9 hundreds digit of the product)

5 x 3 + 3 = 18 (take 8 as thousands digit of the product, carry over 1)

0 x 3 + 5 = 5; 5 + 1 = 6 (take 6 as ten thousands digits of the product)

So, 5301 x 13 = 68913

 

Example 3: 756 x 13

Append 0 before and after: 07560

6 x 3 + 0 = 18 (take 8 as ones digit of the product, carry over 1)

5 x 3 + 6 = 21; 21 + 1 = 22 (take 2 as tens digit of the product, carry over 2)

7 x 3 + 5 = 26; 26 + 2 = 28 (take 8 as hundreds digit of the product, carry over 2)

0 x 3 +7 = 7; 7 + 2 = 9 (take 9 as the thousands digit of the product).

So, 756 x 13 = 9828.

In the next post, we are going to examine why this trick works. For now, go to your friends and impress them with it.