3 Decomponha os seguintes números em fatores primos: a) 8! R.: 27 x 32 x 5 x 7. b) 12! R.: 210 x 35 x 52 x 7 x 11. c) 24! R.: 222 x 310 x 54 x 7...

a) 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 2³ x 2 x 3 x 5 x 2² x 7 x 2 x 3 x 2 = 2⁷ x 3² x 5 x 7 = 128 x 9 x 5 x 7 = 27 x 32 x 5 x 7 b) 12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 2² x 3 x 2 x 5 x 2³ x 7 x 2 x 3² x 2² x 11 = 2¹⁰ x 3³ x 5² x 7 x 11 = 210 x 35 x 52 x 7 x 11 c) 24! = 24 x 23 x 22 x ... x 3 x 2 x 1 = 2³ x 3 x 2² x 11 x 2 x 13 x 2² x 17 x 19 x 2³ x 23 x ... x 3 x 2 x 1 = 2¹⁰ x 3⁴ x 5² x 7 x 11 x 13 x 17 x 19 x 23 = 2²² x 3¹⁰ x 5² x 7³ x 11² x 13 x 17 x 19 x 23 = 222 x 310 x 54 x 73 x 112 x 13 x 17 x 19 x 23