66 : n = c₁ rest 6 ⇒ n = ( 66 - 6 ) : c ₁
142 : n = c₂ rest 7 ⇒ n = ( 142 - 7 ) : c₂
113 : n = c₃ rest 8 ⇒ n = ( 113 - 8 ) : c₃
____________________________
n = 60 : c₁ = 135 : c₂ = 105 : c₃ = cmmdc al numerelor 60; 135 si 105
60 = 2² × 3 × 5
135 = 3³ × 5
105 = 3 × 5 × 7
_______________
cmmdc al numerelor ( 60; 135 si 105 ) = 3 × 5 = 15
n = 15 → impartitorul
Verific:
66 : 15 = 4 rest 6
142 : 15 = 9 rest 7
113 : 15 = 7 rest 8
Raspuns: n = 15 ( impartitorul )
