Question

А) 32 и 24; б) 17 и 51. 4. Найдите НОД. а) 26 и 58; б) 72 и 16. сделайте столбиком плиз

Answer 1

17*1=51÷3; 51÷1=17÷1; 72÷8=16÷2

Answer 2

Calculating the Greatest Common Divisor (GCD)

a) 32 and 24: To find the greatest common divisor (GCD) of 32 and 24, we can use the Euclidean algorithm. The Euclidean algorithm is based on the principle that the GCD of two numbers does not change if the larger number is replaced by its difference with the smaller number.

The calculation can be shown as follows: ``` 32 = 24 * 1 + 8 24 = 8 * 3 + 0 ``` Therefore, the GCD of 32 and 24 is 8.

b) 17 and 51: To find the GCD of 17 and 51, we can use the same Euclidean algorithm: ``` 51 = 17 * 3 + 0 ``` Therefore, the GCD of 17 and 51 is 17.

GCD Calculation in Column Form

a) 26 and 58: Using the Euclidean algorithm in column form: ``` 58 | 26 | 2 26 | 2 | 13 2 | 0 | ``` The GCD of 26 and 58 is 2.

b) 72 and 16: Using the Euclidean algorithm in column form: ``` 72 | 16 | 4 16 | 0 | ``` The GCD of 72 and 16 is 16.