Divisibility rules are quick tests to determine if one number can be divided evenly by another. Examples include: even numbers are divisible by 2, numbers ending in 0 or 5 are divisible by 5, and if the sum of the digits is divisible by 3, the number is divisible by 3. Some rules are more complicated, like those for 7 and 8.
Divisibility rules can be simple, easy-to-remember tests you can run on a number to determine whether it will be divided equally by another number. Some of these rules are quick to memorize and you probably already know them. For example, if the last digit of a number is even, chances are you know that the number can be divided evenly by 2. Another of the divisibility rules that most people might know without thinking about it is that numbers ending in 0 will always be divisible by 10 and by 5.
You can apply the following divisibility rules to numbers to help you determine if you’ll get an even result:
A number is divisible by 3 if the sum of the digits is divisible by 3.
Example: 228 is evenly divisible by 3 because 2 + 2 + 8 = 12 and 12 is divisible by 3.
4 divides a number evenly if the last two digits of that number are divisible by 4.
Example: 788 is divisible by 4 because 88 is divisible by 4.
Any number ending in 0 or 5 will be divided evenly by 5, and 10 will divide any number ending in 0 equally.
If a number is divisible by 2 and 3, it is also divisible by 6.
Example: 180/2 = 90 and 180/3 = 60. So 6 will also divide 180 equally with a result of 30.
When the sum of the digits of a number equals a number divisible by 9, that number will always be divisible by nine.
Example: The number 621 has a sum of digits of 9. 9 will divide 621 equally with a result of 69.
You can take these rules of divisibility by 9 to determine whether 18 will divide numbers evenly. If both 2 and 9 divide a number, 18 will also divide it.
The above examples are probably the easiest divisibility rules to remember. Others get significantly more complicated and may involve multiple manipulations of a number before deciding if it can be divided equally by a divisor. Sometimes it takes less time to simply do a division than to apply one of the divisibility rules to a number, and these rules exist even for very large numbers. With complicated operations you can determine things like whether 71 or 79 will divide other numbers equally.
The divisibility rules by 8 and 7 fall into this more complicated arena. For some mathematical applications they may be useful. However, with smaller numbers you may simply want to do the division to determine whether 8 or 7 are factors of these numbers.
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