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Divisible by 4

This little math trick will show you whether a number is divisible by four or not

So, this is how it works.

Let’s look at 1234
Does 4 divide evenly into 1234?

Well for 4 to divide into any number we have to make sure that the last number is even. If it is an odd number, there is no way it will go in evenly.
So, for example, 4 will not go evenly into 1233 or 1235

So now we know that for 4 to divide evenly into any number the number firstly has to end with an even number.

Back to the question…

4 into 1234

What you do is this:

Take the last number and add it to 2 times the second last number.

If 4 goes evenly into this number then you know that 4 will go evenly into the whole number.

So
4 + (2 X 3) = 10
4 goes into 10 two times with a remainder of 2 so it does not go in evenly.

Therefore 4 into 1234 does not go in completely.

Lets try 4 into 3436546
So, from our example, take the last number, 6 and add it to twice the penultimate number, 4

6 + (2 X 4) = 14
4 goes into 14 three times with two remainder.
So it doesn’t go in evenly.

Let’s try one more.

4 into 212334436

6 + (2 X 3) = 12
4 goes into 12 three times with 0 remainder.

Therefore 4 goes into 234436 evenly.

This entry was posted on Wednesday, January 2nd, 2008 at 4:20 pm and is filed under Mental Tips & Tricks, Vedic Maths. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

2 Responses to “Divisible by 4”

  1. Since 100 is evenly divisible by 4, you can simply look at the last 2 digits. If that number is divisible by 4, then the entire number is as well.

    Most people are fairly good at determining if a two-digit number is divisible by 4. But if you are not: divide the 2-digit number in half and then see if you are able to divide it evenly in half again (in other words, “is the result of dividing that 2-digit number in half an even number?”).

    For example: Is 1234 divisible by 4? Most people can look and see that 34 is not divisible by 4, so 1234 is not divisible by 4. Otherwise, 34/2=17 and 17 is not an even number. So 1234 is not divisible by 4.

    Last example: 234436? Most know that 36 is divisible by 4, so 234436 is also. 36/2=18 and 18 is even, so 36, and therefore 234436, is divisible by 4.

  2. Hi Jim,

    thank you for your clear instructions. It’s a great method you’ve described and I hope others will like it too.

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