Question

Determine o MDC dos dados a seguir,usandoo processo de fatoração simultânea.a) mdc (34,39)b) mdc (48,60)c) mdc (84,140)d) mdc (64,80,96)e) mdc (27,90,108)f) mdc (52,130,156)

Answer 1

(34, 39) ÷ 2 = 17, 39 ÷ 3 = 17, 13 ÷ 17 = 1, 13 ÷13 = 1,1 ou seja: nenhum divisor comum além de 1.

(48, 60) ÷ 2 = 24, 30 ÷ 2 = 12, 15 ÷2 = 6, 15 ÷ 3 = 2, 5 ÷ 2 = 1, 5 ÷ 5 = 1, 1 ou seja divisores comuns: 2²·3

(84, 140) ÷ 2 = 42, 70 ÷ 2 = 21, 45 ÷ 3 = 7, 15 ÷ 3 = 7, 5 ÷ 5 = 7, 1 ÷ 7 = 1, 1 ou seja divisores comuns:  2²·3

(64, 80, 96) ÷ 2 = 32, 40, 48 ÷ 2 = 16, 20, 24 ÷ 2 = 8, 10, 12 ÷ 2 = 4, 5, 6 ÷ 2 = 2, 5, 3 ÷ 2 = 1, 5, 3 ÷ 3 = 1, 5, 1 ÷ 5 = 1, 1, 1 ou seja divisores comuns: 2^4

(27, 90, 108) ÷ 2 = 27, 45, 54 ÷ 2 = 27, 45, 27 ÷ 3 = 9, 15, 9 ÷ 3 = 3, 5, 3 ÷ 3 = 1, 5, 1 ÷ 5 = 1, 1, 1 ou seja divisores comuns: 3²

(52, 130, 156) ÷ 2 = 26, 65, 78 ÷ 2 = 13, 65, 39 ÷ 3 = 13, 65, 13 ÷ 5 = 13, 13, 13 ÷ 13 = 1, 1, 1 ou seja divisores comuns: 2·13