### An introduction to divisibility rules

In this article I will discuss how you can quickly tell if an integer is divisible by 4, 5, 8, or 10. The reason that the numbers are not in order is because the tricks for 4 and 8 are very similar and the tricks for 5 and 10 are almost identical. People often find that the hardest of these tricks to use is the trick for 8. Keep at it and you will soon be able to quickly find out if 4, 5, 8, and/or 10 are factors of any given number. Good luck!

### How to tell if an integer is divisible by 4!

Look at the last two digits of the number. If the two digit number created by the last two digits of the number is divisible by 4 then the number is divisible by 4. In other words, the last two digits will always determine if 4 is a factor of the number.

Examples:

The last two digits of 544 make the number 44. 4 is a factor of 44 because 4 * 11 = 44 therefore 4 is a factor of 544 as well.

4 is not a factor of 84238 because 4 is not a factor of 38. You can quickly tell that 4 is not a factor of 38 since 38 is between 36 and 40, which are two consecutive multiples of 4.

### How to tell if an integer is divisible by 8!

This one is a bit more difficult, but it is very similar to the rule for 4. Look at the last three digits of the number. If the number made by the last three digits is divisible by 8 then the number is divisible by 8.

Examples:

9853 is not divisible by 8 because 853 is not divisible by 8.

8 is a factor of 98864 because 864 is divisible by 8. You can quickly decide that 8 is a factor of 8 64 by breaking down 864 into 800 + 64. 8 is a factor of 800 (8 * 100 = 800) and it is a factor of  64 (8 * 8 = 64), therefore 8 is a factor of 864.

Another way to check if a number is divisible by 8 is to check if you can cut its last three digits in half three times and get another integer each time.

Example, half of 864 is 432, half of 432 is 216, and half of 216 is 108. Clearly this can be difficult with certain numbers, especially large ones, but with more practice you can quickly figure out if a number is divisible by 8.

### How to tell if an integer is divisible by 5!

This is one of the easiest tricks in the book and you probably know it already. An integer is divisible by 5 if its final digit is 5 or 0.

### How to tell if an integer is divisible by 10!

This is the easiest trick in the book. A number is divisible by 10 if it ends with a 0. There is nothing more to it than that.

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