Question

your student maricela asks you why the divisibility of 3 rule works. what is the divisibility rule of 3 and what would you tell her? why does it work?

Answer #1

I tell her with following explanation like this way

Let's take any random number. So for the sake of simplicity,
assume a three digit number **abc.** [eg. 583]

**abc** could literally be any number! This
**abc** is intrinsically written as:

**a***100 + **b***10 +
**c***1.

we can rewrite this as

**abc = a*(1 + 99) + b*(1 + 9) + c**

Using the distributive property of multiplication, you get:

**abc = a.99 + b.9 + a + b + c**

Now, 99a and 9b are obviously divisible by 3.

So the entire sum is divisible by three if and only if (a + b + c) is divisible by 3.

**Divisibility rule of 3:**

If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

A N-digit number was just simply reduced to addition of digits only and thus to identify whether it is divisibility by 3 or not in simplest way.

It is used for testing or checking the number divisible by 3 or not.

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