Which rule applies to determine if a number is divisible by 3?

To determine if a number is divisible by 3, the rule states that the sum of its digits must be divisible by 3. This is derived from the properties of the number system, where any integer can be expressed in terms of its digits and their place values.

When you sum the digits of a number, the total gives you an equivalent modulo 3 result as the original number. For instance, if you take the number 123, the sum of its digits is 1 + 2 + 3 = 6, which is divisible by 3. Therefore, 123 is also divisible by 3. This method simplifies the process of checking for divisibility, especially for larger numbers.

The other options do not correctly represent the divisibility rule for 3. The last digit being zero does not guarantee divisibility by 3, an even number is not necessarily divisible by 3, and not all digits needing to be 3 is an incorrect condition for divisibility. Thus, the sum of the digits must indeed be divisible by 3 to ascertain if the entire number meets the criteria for divisibility by 3.