Suppose that a, m, and n are positive integers and that m is a factor of n. Explain why a % m = (a % n) % m.
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus