Yes, 0 is divisible by 3.
Understanding Divisibility
Divisibility means that a number can be divided by another number without leaving a remainder. In mathematical terms, a number a is divisible by a number b if there exists an integer k such that a = bk*.
Why 0 is Divisible by 3
When we divide 0 by 3, the result is 0. 0 is an integer. Therefore, the definition of divisibility is satisfied. This applies to any non-zero integer; 0 is divisible by any non-zero integer.
- Example: 0 = 3 0. Here, k* = 0, which is an integer.
Several sources confirm this:
- Source 1: "Zero divided by three is, of course, zero, which is an integer; therefore zero is divisible by 3." [Source: Various online forums and discussions]
- Source 2: "Yes, 0 is divisible by any number, including 3. If you divide 0 by 3, the quotient is 0, which indicates that 0 is divisible by 3." [Source: CK-12 Foundation]
This concept is consistent across various mathematical contexts and programming scenarios, as seen in multiple examples found across online forums and Q&A sites. The divisibility rule for 3 focuses on the sum of digits, but it doesn't exclude the case of 0, where the sum of digits is also 0 (a multiple of 3).
