How did Leonhard Euler disprove Pierre de Fermat’s claim about all Fermat numbers being prime?

Pierre de Fermat conjectured that all numbers of the form $2^{2^n}+1$ are prime because the formula yielded prime numbers for values of $n$ from 0 through 4.12

The Swiss mathematician Leonhard Euler disproved this conjecture by demonstrating that the case for $n=5$ is not prime. Specifically, Euler showed that the number $2^{2^5}+1$ (which equals $2^{32}+1$, or 4,294,967,297) is divisible by 641. By splitting this number into the product of 641 and 6,700,417, Euler proved that the value is composite, thereby invalidating Fermat’s assertion.134