Why does the summation of the digits of a number divisible by 3 also become divisible by 3?

Question

Why does the summation of the digits of a number divisible by 3 also become divisible by 3?

In: Mathematics

Answer 1

Because 9 is divisible by 3.

If you have 10, you overshot 9 by 1. If you have 11-19, add this 1 to the second digit and you’ll see if the whole thing is divisible by 3.

If you have a multiple of 10, like 20, 30, 40… you overshot 9 2, 3, 4,… times. So add the number 2, 3, 4…. to the second digit.