$N = p * q$
$p$ & $q$ are primes.
You know $p'$ & $q'$ such at
$N' = p' * q'$ where $N$ divides $N'$
If there a way to proceed from here to get $p$ & $q$?
2026-04-04 06:02:08.1775282528
Factoring a number $N = p * q$ when you have have found $n$, $p'$,$q'$ such that $n*N = p' * q'$
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If $p'$ and $q'$ are the result of a variant of Fermat's method, $\gcd(p',N)$ gives a nontrivial factor of $N$ which is in this case already one of the prime factors of $N$. However if $p'$ and $q'$ are just random numbers with this property, this won't help in general.