Question

Impartind numerele 131,284,197 la acelas numar natural nenul se obtin resturile 7,5 si 11 si caturile nenule. Aflati impartitorul.

Answer 1

131 : X = a rest 7
131 = aX + 7 ==> aX = 131-7 = 124

284 : X = b rest 5
284 = bX + 5 ==> bX = 284-5 = 279

197 : X = c rest 11
197 = cX + 11 ==> cX = 197 - 11 = 186

124 = 2^2 × 31
279 = 3^2 × 31
186 = 2 × 3 × 31
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c.m.m.d.c = 31
deci X = 31 (impartitorul)

131 : 31 = 4 rest 7
284 : 31 = 9 rest 5
197 : 31 = 6 rest 11