Question

НОД(105;924)

Answer 1

есть такое правило

домустим а=105

б=924

ты вычетаешь из большего меньньшее, до тех пор, пока оно не станет меняше, потом опять... пока они не станут равны. полученное число и есть НОД

 

вот решение

а=105 б=924

б=924-105=819

б=819-105=714

714-105=609

609-105=504

504-105=399

399-105=294

294-105=189

189-105=84

так как 105 больше 84, то

а=105-84=21

теперь 84 больше 21

б=84-21=63

б=63-21=42

б=42-21=21

а=б значит НОД=21

 

 

Answer 2

Calculating the Greatest Common Divisor (GCD) of 105 and 924

The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. To calculate the GCD of 105 and 924, we can use various methods, including prime factorization, Euclid's algorithm, or the binary method. Let's use the information from the search results to find the GCD.

From the search results, we can see that the GCD of 105 and 924 is 21.

Using Euclid's Algorithm

Euclid's algorithm is a method for finding the GCD of two numbers. It involves repeatedly replacing one of the numbers with the remainder of the division of the two numbers until the remainder is 0. The other number at this point is the GCD.

Using Euclid's algorithm, we can calculate the GCD of 105 and 924 as follows: - 924 = 8 * 105 + 84 - 105 = 1 * 84 + 21 - 84 = 4 * 21 + 0

Since the remainder is 0, the GCD of 105 and 924 is 21.

Conclusion

Therefore, the greatest common divisor (GCD) of 105 and 924 is 21. This means that 21 is the largest positive integer that divides both 105 and 924 without leaving a remainder.