DIVISIBILITY:
Let xy be the number where y is the unit number and x be the rest of the number.
Ex: 52, y = 2 and x = 5
125, y = 5 and x = 12



The number is divisible by 7 if: (x + 5y) is divisible by 7 Ex: 448 is divisible by 7
5 x 8 + 44 = 84,
which is divisible 7

The number is divisible by 11 if: (x - y) is divisible by 11 Ex: 132is divisible by 11
13 – 2 = 11,
which is divisible 11

The number is divisible by 13 if: (x + 4y) is divisible by 13
Ex: 104 is divisible by 13
10 + 4 (4) = 26,
which is divisible 13

The number is divisible by 17 if: (x – 5y) is divisible by 17 Ex: 136 is divisible by 17
13 – 5(6) = -17,
which is divisible 17

The number is divisible by 19 if: (x + 2y) is divisible by 19 Ex: 133 is divisible by 19
13 + 2(3) = 19,
which is divisible 19

The number is divisible by 23 if: (x + 7y) is divisible by 23 Ex: 207 is divisible by 23
20 + 7(7) = 69,
which is divisible 23

The number is divisible by 29 if (x + 3y) is divisible by 29 Ex: 203 is divisible by 29
20 + 3(3) = 29,
which is divisible 29


Taha