RSA: revealing the modulus factorization by choosing a bad message
Firstly, it's not co-prime to the modulus, so $\gcd(m,N)$ would be greater than $1$. 

Secondly, $N$ is the product of two (and only two) prime numbers $p$ and $q$, so if $\gcd(m,N)&gt;1$, then you know $m$ is one of the factors (and prime factors) of $N$.