Question

Нод(250;400) нод(42;105) нод(500;600) нод(66;77) нод(51;95) нод(41;67) нод(1092;2574)

Answer 1

Ответ:

НОД(250,400)=2*5*5=50

250=2*5*5*5

400=2*2*2*2*5*5

Одинаковые множители это-2,5,5.

НОД(42,105)=3*7=21

42=2*3*7

105=3*5*7

Одинаковые множители это-3,7.

НОД(500,600)=2*2*5*5=100

500=2*2*5*5*5

600=2*2*2*3*5*5

Одинаковые множители это-2,2,5,5.

НОД(66,77)=11

77=7*11

66=2*3*11

Одинаковые множители это-11

НОД(51,95)=1

51=3*17

95=5*19

51 и 95-простые числа!поэтому они имеют только один делитель это 1

НОД(41,67)=1

41=41

67=67

41 и 67-простые числа!поэтому они имеют только один делитель это 1

НОД(1092,2574)=2*3*13=78

1092=2*2*3*7*13

2574=2*3*3*11*13

Одинаковые множители это-2,3,13

Удачной вам учебы!

Answer 2

Finding the Greatest Common Divisor (GCD) using the Euclidean Algorithm

To find the greatest common divisor (GCD) of two numbers, we can use the Euclidean algorithm. The Euclidean algorithm is an efficient method for finding the GCD of two numbers by repeatedly dividing the larger number by the smaller number and taking the remainder. We continue this process until the remainder is zero, at which point the GCD is the last non-zero remainder.

Let's calculate the GCD for the given numbers:

1. GCD(250, 400): To find the GCD of 250 and 400, we can use the Euclidean algorithm. We divide 400 by 250, which gives a quotient of 1 and a remainder of 150. Then, we divide 250 by 150, which gives a quotient of 1 and a remainder of 100. Finally, we divide 150 by 100, which gives a quotient of 1 and a remainder of 50. Since the remainder is not zero, we continue dividing. We divide 100 by 50, which gives a quotient of 2 and a remainder of 0. Since the remainder is now zero, the GCD is the last non-zero remainder, which is 50. Therefore, GCD(250, 400) = 50.

2. GCD(42, 105): To find the GCD of 42 and 105, we can use the Euclidean algorithm. We divide 105 by 42, which gives a quotient of 2 and a remainder of 21. Then, we divide 42 by 21, which gives a quotient of 2 and a remainder of 0. Since the remainder is now zero, the GCD is the last non-zero remainder, which is 21. Therefore, GCD(42, 105) = 21.

3. GCD(500, 600): To find the GCD of 500 and 600, we can use the Euclidean algorithm. We divide 600 by 500, which gives a quotient of 1 and a remainder of 100. Then, we divide 500 by 100, which gives a quotient of 5 and a remainder of 0. Since the remainder is now zero, the GCD is the last non-zero remainder, which is 100. Therefore, GCD(500, 600) = 100.

4. GCD(66, 77): To find the GCD of 66 and 77, we can use the Euclidean algorithm. We divide 77 by 66, which gives a quotient of 1 and a remainder of 11. Then, we divide 66 by 11, which gives a quotient of 6 and a remainder of 0. Since the remainder is now zero, the GCD is the last non-zero remainder, which is 11. Therefore, GCD(66, 77) = 11.

5. GCD(51, 95): To find the GCD of 51 and 95, we can use the Euclidean algorithm. We divide 95 by 51, which gives a quotient of 1 and a remainder of 44. Then, we divide 51 by 44, which gives a quotient of 1 and a remainder of 7. Finally, we divide 44 by 7, which gives a quotient of 6 and a remainder of 2. Since the remainder is not zero, we continue dividing. We divide 7 by 2, which gives a quotient of 3 and a remainder of 1. Finally, we divide 2 by 1, which gives a quotient of 2 and a remainder of 0. Since the remainder is now zero, the GCD is the last non-zero remainder, which is 1. Therefore, GCD(51, 95) = 1.

6. GCD(41, 67): To find the GCD of 41 and 67, we can use the Euclidean algorithm. We divide 67 by 41, which gives a quotient of 1 and a remainder of 26. Then, we divide 41 by 26, which gives a quotient of 1 and a remainder of 15. Finally, we divide 26 by 15, which gives a quotient of 1 and a remainder of 11. Since the remainder is not zero, we continue dividing. We divide 15 by 11, which gives a quotient of 1 and a remainder of 4. Finally, we divide 11 by 4, which gives a quotient of 2 and a remainder of 3. Since the remainder is not zero, we continue dividing. We divide 4 by 3, which gives a quotient of 1 and a remainder of 1. Finally, we divide 3 by 1, which gives a quotient of 3 and a remainder of 0. Since the remainder is now zero, the GCD is the last non-zero remainder, which is 1. Therefore, GCD(41, 67) = 1.

7. GCD(1092, 2574): To find the GCD of 1092 and 2574, we can use the Euclidean algorithm. We divide 2574 by 1092, which gives a quotient of 2 and a remainder of 390. Then, we divide 1092 by 390, which gives a quotient of 2 and a remainder of 312. Finally, we divide 390 by 312, which gives a quotient of 1 and a remainder of 78. Since the remainder is not zero, we continue dividing. We divide 312 by 78, which gives a quotient of 4 and a remainder of 0. Since the remainder is now zero, the GCD is the last non-zero remainder, which is 78. Therefore, GCD(1092, 2574) = 78.

To summarize, the greatest common divisors (GCDs) for the given numbers are as follows: - GCD(250, 400) = 50 - GCD(42, 105) = 21 - GCD(500, 600) = 100 - GCD(66, 77) = 11 - GCD(51, 95) = 1 - GCD(41, 67) = 1 - GCD(1092, 2574) = 78

I hope this helps! Let me know if you have any further questions.