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Vorlesungsmitschrift 05-GSD-MATH01.VL01 Elementarmathematik
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Algorithmen (Algorithmen)
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10.12.20207 Algorithmen
TeilerundVielfache
99TundKgUdurchHasse Diagramme bestimmen
54
a 18 K TatundTn passendübereinander legen
g 4
3 2 3 2 9976 amweitestenobenstehendeTeiler
1
hgk108 n ausgehendvon a und bFigurerweitern
54
27 18 12
4
g
2
EuklidischerAlgorithmus zur Bestimmung ggf amBsp 99T46940,3822
a wie oftGehtderRest invorhergehenden Divisor
Dividend Quotient Divisor persz
16940 4 3822 1652
3822 2 1652 518
1652 3 518 98
518 5 98 t 28
98 3 28 14
28 2 14 0 28 95
Primfaktorzeitegung ZerlegbareZahlen Primzahlen
Satz JedezerlegbareZahl a ist alsProduktvonPrimzahlendarstellbar
PFZ ist eindeutig Anzahlgenaubestimmbar
BeschreibungPFZdurchTabellen a 168 23 3.7 2 3 5 7 11
3 1 01 0
e und99Tergibtsich aus PFZ
Primfaktorenmarkieren die inbeidenZerlegungenvorkommen
fdiesemiteinandermultiplizieren
Bsp a 20 D 12 a 168 b 180
99720,121 224
fg.EEj3 95 22 3 12
II EI
22inbeiden
a 10 D 12
31inbaden
10 2.5 99710,121 2
12 2.2 3
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