1
$\begingroup$

Find $\gcd(300^{40},2^{57})$ I know how to use Euclidean Algorithm for smaller numbers, but with these large numbers I'm not sure how to do it.

$\endgroup$
  • 2
    $\begingroup$ Note that $300^{40}$ is divisible by $2^{80}$. $\endgroup$ – carmichael561 Mar 1 '16 at 2:49
  • $\begingroup$ This might help: $300^{40}=(2^8+2^5+2^3+2^2)^{40}$ $\endgroup$ – Yeah.. Mar 1 '16 at 2:53
1
$\begingroup$

Prime Factorize Each: $$300^{40}=2^{80}3^{40}5^{80}$$ $$2^{57}=2^{57}$$.

Thus, notice that $2^{57}|300^{40}$, and so the $\gcd$ is $2^{57}$.

In general, when approaching the $\gcd(a^{b}, c^{d})$, the easiest method would be to factorize $a$ and $c$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.