Question

cколько будет НОД чисел (11;333) ?

Answer 1

11|11 333|3
 1|      111|3
           37|37
НОД(11,333)=1

Answer 2

Calculating the Greatest Common Divisor (GCD) of 11 and 333

To calculate the Greatest Common Divisor (GCD) of two numbers, 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. We can apply this algorithm to find the GCD of 11 and 333.

Applying the Euclidean Algorithm:

We start by dividing the larger number by the smaller number and then replacing the larger number with the remainder of the division. We continue this process until the remainder is 0. The last non-zero remainder is the GCD of the original two numbers.

Calculation:

Let's apply the Euclidean algorithm to find the GCD of 11 and 333:

1. 333 ÷ 11 = 30 with a remainder of 3 2. 11 ÷ 3 = 3 with a remainder of 2 3. 3 ÷ 2 = 1 with a remainder of 1 4. 2 ÷ 1 = 2 with a remainder of 0

The last non-zero remainder is 1, so the GCD of 11 and 333 is 1.