Réponse :
Explications étape par étape :
Bonjour
A = 349 272
A = 2 × 174 636
A = 2 × 2 × 87 318
A = 2 × 2 × 2 × 43 659
A = 2 × 2 × 2 × 3 × 14 553
A = 2× 2 ×2 ×3 ×3× 4851
A = 2 ×2 × 2 × 3 × 3 × 3 × 1617
A = 2 × 2 × 2 × 3 × 3 × 3 × 3 539
A = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 7 × 77
A = 2 × 2 × 2 × 3 × 3 × 3 × 3 ×7 × 7 × 11
A = 2³ × 3⁴ × 7² × 11
donc n = 2, m = 4 et p = 2
b)
B = 36 288
B = 2 × 18 144
B = 2 × 2 × 9072
B = 2 × 2 × 2 × 4536
B = 2 × 2 × 2 × 2 × 2268
B = 2 × 2 × 2 × 2 × 2 × 1134
B = 2 × 2 × 2 × 2 × 2 × 2 × 567
B = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 189
B = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 63
B = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 21
B = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 7
B = 2⁶ × 3⁴ × 7¹
donc r = 6 s = 4 et t = 1
c )
N = 2³ × 3³ × 7
349 272 = 2³ × 3⁴ × 7² × 11 et 36 288 = 2⁶ × 3⁴ × 7¹
349 272 = 2³ × 3³× 3 × 7 × 7 × 11 et 36 288 = 2³ × 2³ × 3³ × 3 × 7
349 272 = 2³ × 3³× 7 × 3 × 7 × 11 et 36 288 = 2³ × 3³ × 7 × 2³ × 3
349 272 = N × 3 ×7 × 11 et 36 288 = N × 2³ × 3
donc N est un diviseur de 349 272 et 36 288
