# Thread: Divisiblity test for 3

1. ## Divisiblity test for 3

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

Why is this true. I know it has something to with modulus...

I'm asking because I don't want to just memorize each rule, I wan to be able to just figure it out...

2. Hello,
you might want to look at this website that pretty much explains it all nicely :

Math Forum: Explaining the Divisibility Rules

It is really a property of our positional notation system.

3. Originally Posted by jzellt
If a number is divisible by 3 then if the sum of its digits is divisible by 3.

Why is this true. I know it has something to with modulus...

I don't think Bacterius's link used modulus. For that merely note that every number may be represented in the form $\displaystyle a_0+10a_1+\cdots+10^n a_n$. So, noticing that $\displaystyle 10\equiv 1\text{ mod }3$ we see that $\displaystyle a_0+10a_1+\cdots+10^na_n\equiv a_0+a_1+\cdots+a_1\text{ mod }3$ from where the conclusion follows immediately.