Can it be Divided by x ?

This is the sort of question which you ask yourself time and time again when dealing with numbers in maths problems etc.

Yet very rarely does anyone give you a "formula" for doing this. Normally you are told to use trial and error, or occasionally text books will tell you things such as "you should now see that because 364 is divisible by 7.....". How on earth they worked that one out they never tell you (maybe they used trial and error also!).

Here are formulas for all the numbers from 2 to 10 (I am assuming that you can tell if a number is divisible by 1 or not!):
Is it divisible by? How to do it
2 Any number that ends in 0, 2, 4, 6, or 8 is divisible by 2 (i.e. any "even" number)
3

Add the digits in the number. If this total is divisible by 3 then the number itself will be.

e.g. Is 13581 divisible by 3 ? Yes - add up the digits 1 + 3 + 5 + 8 + 1 and you get the total = 18, as 18 is divisible by 3 (6 times) then so is 13581.

Note that this technique is made even easier as you can keep on adding numbers - e.g. the total was 18, but you can also add these digits together 1 + 8 = 9 (also divisible by 3!)
4

If the number's last two digits are 00 or if they are divisible by 4 then the number itself will be.

e.g. Is 34,216 divisible by 4 ? Yes - take the last 2 digits i.e. 16, as 16 is divisible by 4 then so is 34,216
5 Any number that ends in 0 or 5 is divisible by 5.
6

If the number is even and divisible by 3 then it is also divisible by 6.
7

Multiply the last digit of the number by 2 and subtract it from the remaining digits
if that number is divisible by 7 then the number itself will be also.

e.g. Is 735 divisible by 7 ? Yes - take the last digit (5) and multiply it by 2 which gives 10, now subtract 10 from 73 to give 63 - which is divisible by 7 (assuming you know your 7 times table!)
8 Similar to the technique for 4. If the number's last 3 digits are 000 or if they are divisible by 8 then the number itself will be also.
9 Similar to the techinique for 3. Again add all the digits in the number and if they are divisible by 9 then the number itself will be.
10 Any number that ends in 0 is divisible by 10.