• Many students struggle with the concept of divisibility - below are some general rules as well as a practice sheet with answers.

Testing Divisibility:

End rule: 2, 5, and 10

2 - a number is divisible by 2 if the end number is even: 0,2,4,6,8

5 - a number is divisible by 5 if the end number is 0 or 5

10 - a number is divisible by 10 if the end number is 0

3 is divisible by a number if the sum of its digits are divisible by 3 - 555 - 5+5+5=15 which is divisible by 3 so 555 is divisible by 3

9 is divisible by a number if the sum of its digits are divisible by 9 - 555 - 5+5+5=15 which is not divisible by 9 so 555 is not divisible by 9

The if then rule - 6 and 4

6 - if a number is divisible by both 2 and 3 then it is divisible by 6 - 555 is divisible by 3 because it adds up to 15 and 3 can go into 15 evenly but 2 cannot go into 555 evenly because it is not an even number... so therefore, 555 is not divisible by 6.  If we look at 1,224 - it is divisible by 2 because it is even and it is divisible by 3 because it adds up to 9 which is divisible by 3 so it is therefore divisible by 6.

4 - if the number can be divided by 2 twice then it can be divided by 4

http://cdn.kutasoftware.com/Worksheets/PreAlg/Divisibility%20and%20Factors.pdf