Question

НОД (16; 14)= НОД (92; 138)= НОД (220 ; 165)= НОД (6; 24;36)=

Answer 1

16 = 2 × 2 × 2 × 2

14 = 2 × 7

НОД ( 16; 14 ) = 2

92 = 2 × 2 × 23

138 = 2 × 3 × 23

НОД ( 92; 138 ) = 2 × 23 = 46

220 = 2 × 2 × 5 × 11

165 = 3 × 5 × 11

НОД ( 220; 165 ) = 5 × 11 = 55

6 = 2 × 3

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

НОД ( 6; 24; 36 ) = 2 × 3 = 6

Answer 2

To find the greatest common divisor (НОД) of the given numbers, let's calculate step by step:

1. НОД(16, 14): Using the Euclidean algorithm:

• 16 = 1 * 14 + 2
• 14 = 7 * 2 + 0

The remainder is 0, so the greatest common divisor of 16 and 14 is 2.

2. НОД(92, 138): Using the Euclidean algorithm:

• 138 = 1 * 92 + 46
• 92 = 2 * 46 + 0

The remainder is 0, so the greatest common divisor of 92 and 138 is 46.

3. НОД(220, 165): Using the Euclidean algorithm:

• 220 = 1 * 165 + 55
• 165 = 3 * 55 + 0

The remainder is 0, so the greatest common divisor of 220 and 165 is 55.

4. НОД(6, 24, 36): First, find the greatest common divisor of the first two numbers:

• НОД(6, 24):
  • 24 = 4 * 6 + 0

The remainder is 0, so the greatest common divisor of 6 and 24 is 6.

Now find the greatest common divisor of the result (6) and the third number (36):

• НОД(6, 36):
  • 36 = 6 * 6 + 0

The remainder is 0, so the greatest common divisor of 6 and 36 is 6.

So, the НОД(6, 24, 36) is 6.

In summary, the calculations are as follows:

• НОД(16, 14) = 2
• НОД(92, 138) = 46
• НОД(220, 165) = 55
• НОД(6, 24, 36) = 6