Question

1)НОД (12;18) 2)НОД (21;28)3)НОД (72;56)4)НОД (85;170)5)НОД (120;168)​

Answer 1

1)НОД (12;18); 12 = 2 * 2 * 3; 18 = 2 * 3 * 3; НОД (12; 18) = 2 * 3 = 6

2)НОД (21;28); 21 = 3 * 7; 28 = 2 * 2 * 7; НОД (21; 28) = 7

3)НОД (72;56); 72 = 2 * 2 * 2 * 3 * 3; 56 = 2 * 2 * 2 * 7; НОД (72;56) = 2 * 2 * 2 = 8

4)НОД (85;170); 85 = 5 * 17; 170 = 2 * 5 * 17; НОД (85; 170) = 5 * 17 = 85

5)НОД (120;168)​; 120 = 2 * 2 * 2 * 3 * 5;  168 = 2 * 2 * 2 * 3 * 7; НОД (120; 168) = 2 * 2 * 2 * 3 = 24

Answer 2

To find the greatest common divisor (GCD) of the given pairs of numbers, let's use the Euclidean algorithm.

1. GCD(12, 18): Dividing 18 by 12 gives us a quotient of 1 and a remainder of 6. We can then divide 12 by 6, which gives us a quotient of 2 and a remainder of 0. Since the remainder is 0, we stop here. The last non-zero remainder is 6. Therefore, GCD(12, 18) = 6.

2. GCD(21, 28): Dividing 28 by 21 gives us a quotient of 1 and a remainder of 7. We can then divide 21 by 7, which gives us a quotient of 3 and a remainder of 0. The last non-zero remainder is 7. Therefore, GCD(21, 28) = 7.

3. GCD(72, 56): Dividing 72 by 56 gives us a quotient of 1 and a remainder of 16. We can then divide 56 by 16, which gives us a quotient of 3 and a remainder of 8. Next, we divide 16 by 8, which gives us a quotient of 2 and a remainder of 0. The last non-zero remainder is 8. Therefore, GCD(72, 56) = 8.

4. GCD(85, 170): Dividing 170 by 85 gives us a quotient of 2 and a remainder of 0. The last non-zero remainder is 85. Therefore, GCD(85, 170) = 85.

5. GCD(120, 168): Dividing 168 by 120 gives us a quotient of 1 and a remainder of 48. We can then divide 120 by 48, which gives us a quotient of 2 and a remainder of 24. Finally, we divide 48 by 24, which gives us a quotient of 2 and a remainder of 0. The last non-zero remainder is 24. Therefore, GCD(120, 168) = 24.

To summarize:

1. GCD(12, 18) = 6
2. GCD(21, 28) = 7
3. GCD(72, 56) = 8
4. GCD(85, 170) = 85
5. GCD(120, 168) = 24