10. Znajdź NWD i NWW liczb: a) 84 i 90 b) 270 i 700 C) 735 i 252 d) 294 i 385



Odpowiedź :

Odpowiedź:

a) 84 i 90

84 = [tex]2^{2} * 3^{1} *7^{1}[/tex]

90 = [tex]2^{1} * 3^{2} *5^{1}[/tex]

NWD (84, 90) = [tex]2*3=6[/tex]

NWW (84, 90) = [tex]2^{2} *3^{2} *5*7[/tex] = 1260

b) 270 i 700

270 = [tex]2^{1} *3^{3} *5^{1}[/tex]

700 = [tex]2^{2} *5^{2} *7^{1}[/tex]

NWD (270, 700) = [tex]2*5=10[/tex]

NWW (270, 700) = [tex]2^{2} *3^{3} *5^{2} *7=18900[/tex]

c) 735 i 252

735 = [tex]3^{1} *5^{1} *7^{2}[/tex]

252 = [tex]2^{2}*3^{2} *7[/tex]

NWD (735, 252) = [tex]3*7 =21[/tex]

NWW (735, 252) = [tex]2^{2} *3^{2} *5*7^{2} =8820[/tex]

d) 294 i 385

294 = [tex]2*3*7^{2}[/tex]

385 = [tex]5*7*11[/tex]

NWD (294, 385) = 7

NWW (294,385) = [tex]2*3*5*7^{2}*11=16170[/tex]