Divisibility Rules

For this challenge we will investigate a range of algorithms used to apply some of the most common divisibility rules. We will first focus on the divisibility rule of 3 to introduce the concept of recursion.

Divisibility rule

So, for this challenge we will focus on implementing the divisibility rules using some python scripts without using the DIV (//) or MOD (%) operators. In reality, these operators would be a more elegant way of checking if a number is divisible by another number.

Divisibility Rule for 2

Divisibility rule for 2

Let’s look at the following example: is 378 divisible by 2? Yes because its last digit, 8 is a multiple of 2.

Let’s write a Python a function to implement this divisibility rule for 2:

Divisibility Rule for 3

Divisibility rule for 3

Let’s look at the following example: is 378 divisible by 3?

Our aim is to write a function that takes a number as a parameter and returns whether this number is divisible by 3. To implement this function we will use a recursive function (A function with a call to itself).

Your Task

Your task is to adapt the above algorithms to implement the divisibility rules for 4,5,6.

Divisibility rule for 4

Divisibility rule for 5

Divisibility rule for 6

Extension Task: Divisibility rule for 7

Apply a recursive method to find out is a number is divisible by 7. First you will need to read more about the divisibility rule for 7 on this wikipedia page.