+934 Using difference of squares, \(309^2-147^2=(309-147)(309+147)=(162)(456)\). 162 prime factorizes into \(2*3^4\) and 456 prime factorizes into \(2^3*57\). The prime factorization of their product would be \(2^4*3^4*57\). Therefore 57 is the largest prime factor.
+934 Sorry I just realized that 57 isn't prime...it factors into 3 * 19 which makes 19 the largest prime factor.
