The Magic to Divisibility

The Magic to Divisibility 

      It is still the fourth week of elementary math where we are working with divisibility. I have a few secrets that I would like to share with you that has helped me out and has made math a lot easier and faster. The secret is...how to test numbers to see if they are divisible. 

    We all know that if a number is divisible by 2, the number ends in a even number or if the number is divisible by 5 it ends in a 5 or a 0 but what about 3,4,7 and 8? I will tell you! 

    When we are trying to find if a number is divisible by 3 all we have to do is add the digits in the number and divide by 3. 

           Example: 528    

First, add all the digits: 5 + 2 + 8= 15 

Next, divide 15 by 3= 15/3 = 5 

Then we know 528 is divisible by 3! 

Is the same number is divisible by 4? To find out if it is divisible by four all we have to do is look at the last 2 digits of the number. 

Example: 528

First, we look at the last two digits= 28 

Next, divide 28 by 4= 28/4= 7

Then we know 528 is divisible by 4! 

When trying to find if a number is divisible by 7, it is a little more tricky. We have to first divide the number into sections of 3. We then take the even portions and add them together, then the odd portions and add them together and then subtract the two. Once we have subtracted then we take the number and divide by 7. Don't worry I will show you an example! 

Example: 41002536960

Wow!! That's a huge number!! 

First, separate the number into groups of 3. 41002536960

Next, take the even portions; 536 + 41= 577 

Then the odd portions; 960 + 002= 962

Now subtract the two answers= 962-577 =385 

Finally, take 385/7 = 55 

Yes! We know it is divisible by 7!! You can actually do the same exact steps to find out if it is divisible by 11 and 13. Just change the step where you divide by 7 and change it to 13 or 11. 

Finally, we look at if a number is divisible by 8. This is very easy as well, all we do is look at the last 3 numbers of a given number. 

Example: 5,224

First, find the last three digits in the number

Next, divide that number by 8

224/8 = 28 

So we know that 5,224 is divisible by 8. 

These are some great technique to use with large numbers to see if it is divisible by a particular number.  Hope you enjoyed these new techniques and can apply the magic to your own numbers!