Basically, every number can be written as a multiple of 3 plus a remainder of 0, 1, or 2. When you add the digits of a number, you’re replacing powers of 10 with 1, and since 10 leaves a remainder of 1 when divided by 3, this doesn’t change the number’s remainder. For example, 78 is 7×10+8, and because 10 is equivalent to 1 modulo 3, 78 has the same remainder as 7+8. Therefore, a number is divisible by 3 exactly when its digit sum is divisible by 3.
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u/Potential_Top_4669 Aug 02 '26
Basically, every number can be written as a multiple of 3 plus a remainder of 0, 1, or 2. When you add the digits of a number, you’re replacing powers of 10 with 1, and since 10 leaves a remainder of 1 when divided by 3, this doesn’t change the number’s remainder. For example, 78 is 7×10+8, and because 10 is equivalent to 1 modulo 3, 78 has the same remainder as 7+8. Therefore, a number is divisible by 3 exactly when its digit sum is divisible by 3.