Question

Найдите наибольший общий делитель чисел a и b, если: a = 3*3*5*5*5*7,b = 3*5*5*11; a = 2*2*2*3*5*7,b = 3*11*13. Объясните решение пж.

Answer 1

Ответ:

а=3*3*5*5*5*7

б=3*5*5*11

находим общие множители

а=3*3*5*5*5*7

б=3*5*5*11

наибольший общий делитель - 3*5*5=45

а=2*2*2*3*5*7

б=3*11*13

наибольший общий делитель - 3

Answer 2

Finding the Greatest Common Divisor (GCD)

To find the greatest common divisor (GCD) of two numbers, we can use the prime factorization method. The GCD is the product of the common prime factors of the two numbers.

Let's find the GCD of the given numbers, a and b:

- For a = 3 * 3 * 5 * 5 * 5 * 7 and b = 3 * 5 * 5 * 11: - The prime factorization of a is 3^2 * 5^3 * 7. - The prime factorization of b is 3 * 5^2 * 11. - The common prime factors are 3 and 5^2. - The GCD of a and b is 3 * 5^2 = 75.

- For a = 2 * 2 * 2 * 3 * 5 * 7 and b = 3 * 11 * 13: - The prime factorization of a is 2^3 * 3 * 5 * 7. - The prime factorization of b is 3 * 11 * 13. - The common prime factor is 3. - The GCD of a and b is 3.

Therefore, the GCD of the given numbers is 75 and 3, respectively.