These can be derived by taking successive powers of 10 modulo the number you wish to create a rule for.

A full explanation will have to wait for another day.

Ways of telling whether an integer is divisible by:

### 1

Drop an apple. If it falls downwards, the integer is divisible by 1.

### 2

Yes, if the last digit is divisible by two.

### 3

Yes, if the sum of the digits is divisible by 3.

### 4

Yes, if the last digit of the integer divided by two is divisible by two.

### 5

Yes, if the last digit is a 0 or a 5.

### 6

Divide the integer by 2. Yes, if the sum of the digits of the result is divisible by three.

### 7

Let the digits of the number be where has the lowest place value. The number is divisible by 7 if 7 divides the sum of

**Example:** Does 7 divide 3236655

**Answer:** yes, since

and

and as 7 clearly divides 28, 7 divides 91, hence 7 divides 3236655.

### 9

Yes, if the sum of the digits is divisible by 9.

6:

Divide the integer by 2. Yes, if the sum of the digits of the result is *divisible by* three.

:)

Thanks :D