Sum-of-Digits Divisibility Power!

Ever wondered how to tell if a huge number can be divided perfectly by 3 or 9 WITHOUT a calculator? Your secret superpower is here!

Subject: number-theory • Classes: 6–12 • Difficulty: basic

The Trick

**For Divisibility by 3:** A number is divisible by 3 if the SUM of its digits is divisible by 3. **For Divisibility by 9:** A number is divisible by 9 if the SUM of its digits is divisible by 9. **Why it works:** Every power of $10$ (like $10, 100, 1000$) leaves a remainder of $1$ when divided by $3$ or $9$. For example, $10 = 3 \times 3 + 1$ and $10 = 9 \times 1 + 1$. This means any number $N$ will have the same remainder as the sum of its digits when divided by $3$ or $9$. If the sum has no remainder, $N$ has no remainder!

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