Question

Найти НОД 2 способами 428 и 54 , 232 и 728 , 411 и 25 , 29 и 78

Answer 1

НОД (428 и 54) =2
428 | 2                        54 | 2
214 | 2                        27 | 3
107 | 107                      9 | 3
1     |                            3 | 3
                                    1 |
НОД (232 И 728) = 2
232 | 2                        728 | 2
116 | 2                        364 | 2
  58 | 2                        182 | 2
  29 | 29                        91 | 7
     1|                            13 | 13
                                     1 | 
НОД (411 И 25) = 1
411 | 3                         25 | 5
137 | 137                       5 | 5 
   1 |                              1 |
НОД (29 И 78) = 1
29 | 29                          78 | 2
 1 |                               39 | 3
                                    13 | 13
                                      1 |

Answer 2

Finding the GCD (Greatest Common Divisor) of Two Numbers

To find the greatest common divisor (GCD) of two numbers, there are several methods you can use. Here are two common methods:

Method 1: Euclidean Algorithm

The Euclidean algorithm is a widely used method for finding the GCD of two numbers. It involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero. The GCD is then the last non-zero remainder.

Let's apply the Euclidean algorithm to find the GCD of the given pairs of numbers:

1. For 428 and 54: - Divide 428 by 54: 428 ÷ 54 = 7 with a remainder of 10. - Divide 54 by 10: 54 ÷ 10 = 5 with a remainder of 4. - Divide 10 by 4: 10 ÷ 4 = 2 with a remainder of 2. - Divide 4 by 2: 4 ÷ 2 = 2 with no remainder. - The GCD of 428 and 54 is 2.

2. For 232 and 728: - Divide 728 by 232: 728 ÷ 232 = 3 with a remainder of 32. - Divide 232 by 32: 232 ÷ 32 = 7 with a remainder of 16. - Divide 32 by 16: 32 ÷ 16 = 2 with no remainder. - The GCD of 232 and 728 is 16.

3. For 411 and 25: - Divide 411 by 25: 411 ÷ 25 = 16 with a remainder of 11. - Divide 25 by 11: 25 ÷