this post was submitted on 08 Jan 2025
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Is this a real divisibility rule?
Yep. If the sun of the numbers is divisible by 3, the number is divisible by three.
Works great for 6 too, as if it's divisible by 3 and even, the number is divisible by 6.
And 9 is the same thing, but the sum has to be divisible by 9 (e.g. 12384 is divisible by 9 because the sum of the digits is 18, which is divisible by 9)
There's also good rules for 4 and 8 as well. If the last 2 digits are divisible by 4, the whole number is (e.g. 127924 is divisible by 4 because 24 is) and if the last 3 numbers are divisible by 8, the whole number is (e.g. 12709832 is divisible by 8 because 832 is.)
Now provide the proof
Il do it for disability by three and a three digit numbers with the digits a, b and c. The value of that number then is 100a + 10b + c. They concept is the same for nine.
This means that, mod 3, a three digit number is equivalent to the sum of it's digits and therefore preserves disability by 3.