Question

Найдите наибольший общий делитель чисел способом перебора делителей 12 и 32;30 и 42;35 и 60;

Answer 1

1)
делители 12: 1, 2, 3, 4, 6, 12
делители 32: 1, 2, 4, 8, 16, 32
общие делители: 1, 2, 4
НОД ( 12; 32) = 4

2)
делители 30: 1, 2, 3, 5, 6, 10, 15, 30
делители 42: 1, 2, 3, 6, 7, 14, 21, 42
общие делители: 1, 2, 3, 6
НОД ( 30; 42) = 6
3)
делители 35: 1, 5, 7, 35
делители 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
общие делители: 1, 5
НОД (35: 60) = 5

Answer 2

Finding the Greatest Common Divisor (GCD) by Exhaustive Division

To find the greatest common divisor (GCD) of two numbers by exhaustive division, we can systematically test each potential divisor to find the largest number that divides both numbers without leaving a remainder.

1. GCD of 12 and 32: - The divisors of 12 are 1, 2, 3, 4, 6, and 12. - The divisors of 32 are 1, 2, 4, 8, 16, and 32. - The common divisors are 1, 2, and 4. - Therefore, the GCD of 12 and 32 is 4.

2. GCD of 30 and 42: - The divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. - The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. - The common divisors are 1, 2, 3, and 6. - Therefore, the GCD of 30 and 42 is 6.

3. GCD of 35 and 60: - The divisors of 35 are 1, 5, 7, and 35. - The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. - The common divisor is 5. - Therefore, the GCD of 35 and 60 is 5.

These results are obtained by exhaustively testing the divisors of each number and identifying the largest common divisor.