If the sum of the digits is divisible by 3 then the number is divisible by 3
This statement is a rule in number theory and it is indeed true
This statement is a rule in number theory and it is indeed true. The rule states that if the sum of the digits of a number is divisible by 3, then the original number itself is also divisible by 3.
To understand why this is true, let’s consider a general number. Let’s say we have a three-digit number “abc”, where “a”, “b”, and “c” represent the digits of the number.
The number “abc” can be written as:
abc = 100a + 10b + c.
If we find the sum of the digits, it would be:
a + b + c.
Now, if this sum is divisible by 3, then we can write it as:
a + b + c = 3k, where k is an integer.
Substituting this back into our original equation for “abc”, we get:
abc = 100a + 10b + c = 99a + 9b + (a + b + c) = 9(11a + b) + 3k.
We can see that “abc” is a multiple of both 9 and 3, therefore it is divisible by 3.
This rule can be extended to any number of digits. It is important to note that this rule holds true regardless of the order of the digits. For example, the numbers 123, 321, and 213 all have the same sum of digits (6), so they are all divisible by 3.
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