Divisibility by 3

A whole number is divisible by 3 when the sum of its digits is also divisible by 3. This works because each place value is a multiple of 10, and 10 leaves the same remainder as 1 when divided by 3, so the original number and its digit sum have the same remainder mod 3. That means you can test divisibility quickly without dividing the entire number.

Use this shortcut when checking whether a number can be divided by 3 without a remainder, especially for large numbers. It is also useful in mental math, simplifying fractions, and checking answers in arithmetic problems.

• Forgetting to add all the digits, especially zeros in the middle or at the end
• Stopping after one digit-sum step without checking whether that sum is itself divisible by 3
• Using this test for divisibility by 2, 5, or 9 instead of 3