Question

Найдите:а) НОД(24,48) б) НОД(62,31) В)НОД(132,11) Г)НОД(256,32) Д)НОД(45,15) Е)НОД(26,63) ПОМОГИТЕ ПОЖАЛУЙСТА ДАМ 30 БАЛЛОВ

Answer 1

А) 24
б) 31
в) 11
г) 32
д) 15
е) 1

Answer 2

а) НОД(24,48)

To find the greatest common divisor (НОД) of 24 and 48, we can use the Euclidean algorithm. The Euclidean algorithm states that the greatest common divisor of two numbers is equal to the greatest common divisor of the remainder when the larger number is divided by the smaller number.

In this case, when we divide 48 by 24, the remainder is 0. Therefore, the greatest common divisor of 24 and 48 is 24.

Answer: НОД(24,48) = 24

б) НОД(62,31)

To find the greatest common divisor of 62 and 31, we can again use the Euclidean algorithm. When we divide 62 by 31, the remainder is 0. Therefore, the greatest common divisor of 62 and 31 is 31.

Answer: НОД(62,31) = 31

в) НОД(132,11)

Using the Euclidean algorithm, we can find the greatest common divisor of 132 and 11. When we divide 132 by 11, the remainder is 0. Therefore, the greatest common divisor of 132 and 11 is 11.

Answer: НОД(132,11) = 11

г) НОД(256,32)

Applying the Euclidean algorithm to find the greatest common divisor of 256 and 32, we divide 256 by 32 and get a remainder of 0. Hence, the greatest common divisor of 256 and 32 is 32.

Answer: НОД(256,32) = 32

д) НОД(45,15)

Using the Euclidean algorithm, we divide 45 by 15 and get a remainder of 0. Therefore, the greatest common divisor of 45 and 15 is 15.

Answer: НОД(45,15) = 15

е) НОД(26,63)

Applying the Euclidean algorithm to find the greatest common divisor of 26 and 63, we divide 63 by 26 and get a remainder of 11. Then, we divide 26 by 11 and get a remainder of 4. Finally, we divide 11 by 4 and get a remainder of 3. Therefore, the greatest common divisor of 26 and 63 is 3.

Answer: НОД(26,63) = 3