To simplify \(2278 \div 2276\), we can use the properties of exponents. The expression can be rewritten using the rule \(a^m \div a^n = a^{m-n}\).
Thus,
\[ 2278 \div 2276 = 227^{8-6} = 227^2 \]
So the simplified expression is:
\[ \boxed{227^2} \]