  We present new formulas for computing greatest common divisors (GCDs) and
extracting the prime factors of semiprimes using only elementary arithmetic
operations: addition, subtraction, multiplication, floored division, and
exponentiation. Our GCD formula simplifies a formula of Mazzanti and is derived
using Kronecker substitution techniques from our earlier research. By combining
this GCD formula with our recent result on an arithmetic term for $\sqrt{n}$,
we derive explicit expressions for the prime factors of a semiprime $n=p q$.
