
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
Adding rule: 3 and 9
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