Have you ever wondered why an integer is evenly divisible by 3 if and only if the sum of its digits is divisible by 3?

Of course you have.

Well here's why

Incidentally, this rule is of course recursively applicable.

Take the number 160,851,325,561,311. It's digits sum to 48.

Suppose you don't know from memory that 48 is divisible by 3.

The sum of 4 and 8 is 12, which you probably know is divisible by 3.

But even if you don't, 1 + 2 is 3, which is clearly divisible by three.

#Arithmetic #NumberTheory #Fun

https://www.cuemath.com/questions/prove-that-if-the-sum-of-the-digits-is-divisible-by-3-the-number-is-divisible-by-3/