Question

Правило нахождения НОД.

Answer 1

Учи правила кто согласен жми спосибо

Answer 2

Finding the Greatest Common Divisor (НОД)

The rule for finding the greatest common divisor (НОД) involves determining the largest positive integer that divides each of the numbers without leaving a remainder. This can be done using various methods, such as prime factorization, Euclid's algorithm, or using the division method.

Prime Factorization Method: One way to find the greatest common divisor is by prime factorization. This involves breaking down each number into its prime factors and then identifying the common prime factors along with their lowest powers.

For example: - To find the НОД of 315 and 245: - 315 = 5 * 3 * 3 * 7 - 245 = 5 * 7 * 7 - The common prime factors are 5 and 7, so НОД(315, 245) = 5 * 7 = 35.

- To find the НОД of 236 and 328: - 236 = 2 * 2 * 59 - 328 = 2 * 2 * 2 * 41 - The common prime factors are 2 and 59, so НОД(236, 328) = 2 * 2 * 59 = 236.

Euclid's Algorithm: Another method to find the greatest common divisor is by using Euclid's algorithm, which involves successive division of the two numbers until the remainder is zero. The divisor at this point is the greatest common divisor.

For example: - Using Euclid's algorithm, the НОД of 661 and 113 is found to be 1.

These methods provide effective ways to find the greatest common divisor of two numbers, offering flexibility based on the specific requirements of the problem at hand.

Conclusion

The rule for finding the greatest common divisor (НОД) involves various methods such as prime factorization and Euclid's algorithm. These methods offer effective ways to determine the largest positive integer that divides each of the numbers without leaving a remainder.