Divide 3

111 is divisible by 3.

222 is divisible by 3.

333 is divisible by 3.

444 is divisible by 3.

555 is divisible by 3.

Let \(M\) be a positive integer with all the same digits but none of its digits are 3.

True or false:

If \(M \) has \(N\) digits, where \(N\) is divisible by 3, then \(M\) must be divisible by 3.

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