DIVISIBILITY OF NUMBERS BY 10 to 13

BY 10

The no having 0 in its unit place is divisible by 10.
6679 : 9 is unit digit place ,So 6679 is not divisible by 10.
4570 : 0 is unit digit place ,So 4570 is not divisible by 10.

BY 11

The no whose difference of sum of every other digit
is divisible by 11.
14568:(1+5+8)-(4+6)=4
So it is not divisible by 11.
1331:(1+3)-(1+3)=0
So it is not divisible by 11. 

BY 12

If the number is divisible by 3 and 4, then clearly the number is divisible by 12.
8796540 :8+7+9+6+5+4+0=39 :9+3=12;1+2=3
So it is divisible by 3
Last two digits are 40 which is divisible by 4
So 8796540 is divisible by 12.

Divisibility rule for 13:

Multiply unit place by 4(Key no of 13) add it to rest of the digits.

                                                 for 12468 : 1 2 4 6 8 x 4

                                                                          3 2

                                                                    --------------------
                                                                      1 2 7 8 x 4
                                                                         3 2

                                                                    -------------------
                                                                      1 5 9 x 4 

                                                                      3 6

                                                                    --------------------

                                                                      5 1 

                                                      So 12468 is not divisible by 13