Divisibility by 3: The Sum Game!

Want to know instantly if a HUGE number is divisible by 3? No long division needed! Here's a super-fast trick...

Subject: number-theory • Classes: 6–12 • Difficulty: basic (6-8)

The Trick

A number is divisible by 3 if the sum of its digits is divisible by 3. Why? Because any number can be written as a sum of multiples of 10 plus its digits. Since 10 leaves a remainder of 1 when divided by 3, $10^n$ also leaves a remainder of 1 when divided by 3. So, we only need to check the sum of the digits.

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