Divisibility by 4

100 is divisible by 44. That is why every number formed of hundreds, which ends with two zeros is divisible by 4.

For example 500, 700, 300 are divisible by 4 because they end with two zeros. 6000 and 23 000 are also divisible by 4.

Let us take number which does not end with zeros, but with any other digits. For example 916. This number can be presented like this sum 916 = 900 + 16
Because both addends are divisible by 4, their sum 916 is also divisible by 4

918 is not divisible by 4 because 918 = 900 + 18 , one of the addends(18) is not divisible by 4.

From the examples we can see that the second addend is two-digit number, formed by the last two digits. From that number depends if the whole number can be divided by 4 or not. This is true for every other multi-digit number

So, number 13724 is divisible by 4 because its last two digits express number 24, which is divisible by 4.

13722 is not divisible by 4 because its last two digits express number 22, which is not divisible by 4.

Numbers divisible by 4 are only those which have last two digits zeros or digits which express number divisible by 4.

For example: 450, 2506, 15342, 20018 are not divisible by 4 540, 1256, 32442, 56300 are divisible by 4

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