Question

Find the $g.c.d$ of
$144,233$

Answer 1

144 = 2⁴ × 3²;
233 is a prime number, it cannot be prime factorized into other prime factors;

Take all the common prime factors, by the lowest exponents.
But the two numbers have no common prime factors.

Greatest common divisor:
gcd (144; 233) = 1;