Question

Numerele 641,278,550 impartite la acelas numar natural dau resturile egale cu 11,8 respectiv 10.La ce numar au fost impartite?
AJUTOR!!!

Answer 1

641 : a = x rest 11 ==> ax = 641-11 = 630
278 : a = y rest 8 ==> ay = 278 - 8 = 270
550 : a = z rest 10 ==> az = 550-10 = 540

630 = 2 × 3^2 × 5 × 7
270 = 2 × 3^3 × 5
540 = 2^2 × 3^3 × 5
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c.m.m.d.c = 2 × 3^2 × 5 = 90
a > 11
a = D90 = 15;18; 30; 45; 90

Verificare:
641 : 90 = 7 rest 11
278 : 90 = 3 rest 8
550 : 90 = 6 rest 10