Determine the prime factorization of $25^{2}+72^{2}$.
Let's write $25^{2}+72^{2}=5^{4}+4.6^{4}=\left(5^{2}+2.6^{2}+2.5 .6\right)\left(5^{2}+2.6^{2}-2.5 .6\right)=157.37$. Since 37 and 157 are prime, the result is obtained.