Why Does the Divisibility Rule for 3 Work

Because every power of ten is one off from a multiple of three: 1 is one over 0; 10 is one over 9; 100 is one over 99; 1000 is one over 999; and so on. This means that you can test for divisibility by 3 by adding up the digits: 1×the first digit+1×the second digit+1×the third digit, and so on.

How do you prove divisibility by 3?

The test: A number is divisible by 3 if the sum of all of its digits is divisible by 3. The Proof: Any n digit number can be represented as where is the nth digit starting from the units place. The test: A number is divisible by 3 if the sum of all of its digits is divisible by 3.

Why is a number divisible by 3 if the sum of its digits is divisible by 3?

Divisibility by Three On this page we prove the theorem known from school that an integer is divisible by 3 if and only if the sum of its digits is divisible by 3. … Hence all the numbers bk are divisible by 3. Hence all the numbers ak*bk are divisible by 3. Hence their sum (which is x-s) is divisible by 3.