Yes, a number is divisible by 3 if the sum of its digits is divisible by 3. This rule is a quick way to determine the divisibility of larger numbers without performing the actual division.
For example, consider the number 123. If we add its digits: 1 + 2 + 3 = 6. Since 6 is divisible by 3, we can conclude that 123 is also divisible by 3.
This works because of how the base 10 number system is structured. Each digit represents a power of 10, and since 10 is congruent to 1 modulo 3, the entire number’s divisibility can be determined by the sum of its digits.
In practice, this means that you can quickly check large numbers by just summing their digits. If the result is a multiple of 3, then the original number is also a multiple of 3.