Question

1. Calculati c.m.m.d.c. si c.m.m.mc.
a) 70, 105, 245
6) 72, 108, 144
2 Arătați daca sunt numere prime
a) 81 si 90
b) 40 și 56
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Answer 1

Răspuns:

$1. \\ a)70 =2 \times 5 \times 7 \\ 105 =3 \times 5 \times 7 \\ 245 =5 \times {7}^{2} \\c .m.m.d.c = 5 \times 7 = 35 \\ c.m.m.m.c = 2 \times 3 \times 5 \times {7}^{2} = 2 \times 3 \times 5 \times 49 = 6 \times 5 \times 49 = 30 \times 49 = 1470 \\ 6)72 = {2}^{3} \times {3}^{2} \\ 108 = {2}^{2} \times {3}^{3} \\ 144 = {2}^{4} \times {3}^{2} \\ c.m.m.d.c = {2}^{2} \times {3}^{2} = 4 \times 9 = 36 \\ c.m.m.m.c = {2}^{4} \times {3}^{3} = 16 \times 27 = 432 \\ \\ 2. \\ a)81 \: si \: 90 \: \: \: nu \: sunt \: prime \\ 81 = {3}^{4} \\ 90 = 2 \times {3}^{2} \times 5 \\ b)40 \: si \: 56 \: \: nu \: sunt \: prime \\ 40 = {2}^{3} \times 5 \\ 56 = {2}^{3} \times 7$

sper că te-am ajutat!!!