How do we know if a number is divisible by 3?

You can determine if a number is divisible by 3 by following a simple rule: Add all the digits of the number together. If the sum is divisible by 3, then the original number is also divisible by 3.

For example, let's take the number 456.

1. Add the digits: 4 + 5 + 6 = 15
2. Check if the sum is divisible by 3: 15 is divisible by 3 (15 / 3 = 5).
3. Therefore, the original number 456 is also divisible by 3.

This rule applies to numbers of any size. If the sum of the digits is not divisible by 3, then the original number is not divisible by 3 either.

Let's try another example: 789.

1. Add the digits: 7 + 8 + 9 = 24
2. Check if the sum is divisible by 3: 24 is divisible by 3 (24 / 3 = 8).
3. Therefore, 789 is divisible by 3.

This rule is based on the fact that any number can be expressed as the sum of its digits multiplied by powers of ten. Since 10 leaves a remainder of 1 when divided by 3, any power of 10 also leaves a remainder of 1. This means that the divisibility of a number by 3 depends only on the sum of its digits.