Chapitre 3 Nombres entiers et rationnels

a b b 6= 0
a b
q r
a=b×q+r r < b
q r
521 = 4 ×130 + 1 1<4
a b b 6= 0
b a
n a =n×b
48 = 6 ×8

b a a b
b a a b
5 + 8 + 2 = 15
5 + 6 + 7 = 18 567 = 9 ×63

a b
a b
a b
a b a > b
P GCD(a;b) = P GCD(b;a−b)
165 −66 = 99
99 −66 = 33
66 −33 = 33

a b a > b
P GCD(a;b) = P GCD(b;r)
r a b
1755 = 455 ×3+390
455 = 390 ×1+65
390 = 65 ×6+0

3
20
15
120
165
66 =33 ×5 33 ×2=5 2
455
1755 =65 ×7 65 ×27 =7 27
125
35
125
35 =5×5×5 5×7=5×5 7=25 7