Question

Найдите наибольший общий делитель чисел: 1) 16 и 36 2) 54 и 18 3) 76 и 114 4) 480 и 288 5) 27,72 и 108

Answer 1

1)

16 = 2·2·2·2 = 2⁴

36 = 2·2·3·3 = 2²·3²

НОД(16, 36) = 2² = 4

2)

54 = 2·3·3·3 = 2·3³

18 = 2·3·3 = 2·3²

НОД(54, 18) = 2·3² = 18

3)

76 = 2·2·19 = 2²·19

114 = 2·3·19

НОД(76, 114) = 2·19 = 38

4)

480 = 4·4·30 = 2⁵·3·5

288 = 4·4·18 = 2⁵·3²

НОД(480, 288) = 2⁵·3 = 96

5)

27 = 3·3·3 = 3³

72 = 4·18 = 2³·3²

108 = 4·27 = 2²·3³

НОД(27, 72, 108) = 3² = 9