<prompt> Kwa kuwa n hupanda juu ya nambari kamili, ni thamani gani ya juu zaidi inayowezekana ambayo kigawanyaji kikuu cha kawaida cha 13n 8 na 5n3 kinaweza kuchukua?  <response>: Tunaweza kutumia algorithm ya Euclidean hapa. anzaaligngcd13n8, 5n3 gcd5n3, 13n8-25n3 gcd5n3, 3n 2 gcd3n2, 5n3-3n2 gcd3n2, 2n 1 gcd2n1, 3n2-2n1 gcd2n1, n1 gcdn1, 2n1-n1 gcdn1, n gcdn, n1-n gcdn, 1 1.mwishopanga 