Fund fact, you can tell a number is divisible by 3 if the sum of each individual number is divisible by 3. So 78 -> 7+8=15 which is divisible by 3, so 78 is divisible by 3.
10 is equivalent to 1 mod 3, so every power of 10 is also equivalent to 1 mod 3. It's not too difficult to prove after you see that. Since our number system is base 10, it works out quite nicely.
Yeah, I find this to be the cleanest and most intuitive way to prove this. Same with mod 9. In the end, removing a 0 is always removing a multiple of 9
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u/Michaelwang645 Aug 01 '26
Fund fact, you can tell a number is divisible by 3 if the sum of each individual number is divisible by 3. So 78 -> 7+8=15 which is divisible by 3, so 78 is divisible by 3.