Răspuns:
Salutare!
✳ Pentru a calcula cel mai MARE divizor comun al numerelor vom:
- Descompune în factori primi numerele
- Înmulțim toți factorii primi comuni la puterile cele mai mici
Mecanismul de descompunere:
30 | 2
15 | 5
3 | 3
1 | ⇒ 30 = 2 · 3 · 5
(A) 16, 24, 40
16 = 2⁴
24 = 2³ · 3
40 = 2³ · 5
cmmdc (16,40, 24) = 2³
cmmdc (16,40, 24) = 8
_______________________
(B) 120, 180, 240
120 = 2³· 3 · 5
180 = 2² · 3² · 5
240 = 2⁴ · 3 · 5
cmmdc (120, 240, 180) = 2² · 3 · 5
cmmdc (120, 240, 180) = 60
_______________________
(C) 15, 35, 45
15 = 3 · 5
35 = 5 · 7
45 = 3² · 5
cmmdc (15, 35, 45) = 5
_______________________
(D) 250, 375, 650
250 = 2 · 5³
375 = 3 · 5³
650 = 2 · 5² · 13
cmmdc (250, 375, 650) = 5²
cmmdc (250, 375, 650) = 25
_______________________
(E) 27, 54, 180
27 = 3³
54 = 2 · 3³
180 = 2² · 3² · 5
cmmdc (27, 54, 180) = 3²
cmmdc (27, 54, 180) = 9
_______________________
(F) 144, 156, 192
144 = 2⁴ · 3²
156 = 2² · 3 · 13
192 = 2⁶ · 3
cmmdc (144, 156, 192) = 2² · 3
cmmdc (144, 156, 192) = 4 · 3
cmmdc (144, 156, 192) = 12
_______________________
(G) 28, 49, 63
28 = 2² · 7
49 = 7²
63 = 3² · 7
cmmdc (28, 49, 63) = 7
_______________________
(H) 1020, 595, 1105
1020 = 2² · 3 · 5 · 17
595 = 5 · 7 · 17
1105 = 5 · 13 · 17
cmmdc (1020, 595, 1105) = 5 · 17
cmmdc (1020, 595, 1105) = 85
_______________________
(I) 63, 88, 65
63 = 3² · 7
88 = 2³· 11
65 = 5 · 13
cmmdc (63, 88 65) = 1
