Question

Найдите НОД чисел(56,68)

Answer 1

Может быть 4, но не знаю

Answer 2

Finding the Greatest Common Divisor (GCD) of 56 and 68

To find the greatest common divisor (GCD) of two numbers, we can use various methods such as prime factorization, Euclidean algorithm, or using a calculator or programming language. Let's explore the different methods and find the GCD of 56 and 68.

Method 1: Prime Factorization

One method to find the GCD is by using prime factorization. We can express both numbers as products of their prime factors and then find the common factors.

The prime factorization of 56 is 2^3 * 7, and the prime factorization of 68 is 2^2 * 17.

To find the GCD, we take the product of the common prime factors raised to the lowest power. In this case, the common prime factor is 2, raised to the power of 2 (the lowest power it appears in both numbers).

Therefore, the GCD of 56 and 68 is 2^2 = 4.

Method 2: Euclidean Algorithm

Another method to find the GCD is by using the Euclidean algorithm. The algorithm involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero. The last non-zero remainder is the GCD.

Let's apply the Euclidean algorithm to find the GCD of 56 and 68:

1. Divide 68 by 56: 68 ÷ 56 = 1 remainder 12 2. Divide 56 by 12: 56 ÷ 12 = 4 remainder 8 3. Divide 12 by 8: 12 ÷ 8 = 1 remainder 4 4. Divide 8 by 4: 8 ÷ 4 = 2 remainder 0

Since the remainder is now zero, the GCD of 56 and 68 is the last non-zero remainder, which is 4.

Conclusion

Using both the prime factorization method and the Euclidean algorithm, we found that the GCD of 56 and 68 is 4.