Divisibility Tests
There are many occasions when it is helpful to know if an integer (a whole number) is exactly divisible by another number.
All the numbers in the following examples were generated randomly when the page loaded. To see a different set of numbers, refresh the page or press F5.
Prime numbers are shown in the shaded boxes. These are the numbers to be tested for in Factor trees.
Testing for divisibility by 2
Checking whether any number is divisible by 2 is very easy. Simply look at the digit in the units column. If it is an even number then the whole number is divisible by 2.
Testing for divisibility by 3
Checking whether any number is divisible by 3 is also fairly straightforward. In this case the method is a little different; add all the digits making the number together. If the total for the digits is a multiple of 3 then the whole number is also divisible by 3.
Testing for divisibility by 4
When testing a number for divisibility we only need to look at the final two digits. This is because 100, 200, etc and any other multiple of 100 is always divisible by 4. Only the part of the number in the tens and units columns needs to be checked.
Testing for divisibility by 5
One of the easiest numbers to check is 5. Simply check the final digit. If the number ends with a 0(zero) or a 5 then it is divisible by 5.
Testing for divisibility by 6
For a number to be divisible by 6 it must be divisible by both 2 and 3. Apply both the tests described above.
Testing for divisibility by 7
Testing a number to see if 7 is a factor is more difficult. The rule is:
Double the units and subtract the answer from the number of tens. Repeat this process as many times as possible. The number you started with is divisible by 7 if you finish the sequence with a 0(zero) or a number obviously divisible by 7.
There are other ways of testing for divisibility by 7 based on modular arithmetic but the easiest to apply has been used here.
Testing for divisibility by 8
Checking a number for divisibility by 8 is also a bit tricky. 1000, 2000 and any multiple of 1000 is divisible by 8. This means that we only need to examine the last three digits. If the number formed from the last three digits is divisible by 8, then so is the original number.
This will require a short division sum to check which seems a lot of work! Fortunately, we do not need to worry about divisibility by 8 for factor trees.
Testing for divisibility by 9
This works in a similar way to divisibility by 3. Add up all of the digits in a number. If the total is divisible by 9 then so is the original number.
Tesing for divisibility by 10
Like 5, divisibility by 10 is very straightforward. Any number ending in a 0(zero) is divisible by 10.
Testing for divisibility by 11
Like 7, divisibility by 11 has a more complex test using the rule:
Alternately subtract and add the digits working from left to right. If the result is 0(zero) or a number divisible by 11 then the original number is also divisible by 11.
There are tests that can be applied for other numbers too, but these are the most commonly used in Factor trees.