Question

Знайди найбільший спільний дільник чисел 55і132

Answer 1

Это 11
И 55 делится на 11, и 132 , если брать числа 22,33,44 эти числа не поделятся на 55

Answer 2

Finding the Greatest Common Divisor (GCD) of 55 and 132

To find the greatest common divisor (GCD) of two numbers, we can use the method of prime factorization or the Euclidean algorithm. In this case, we'll use the Euclidean algorithm to find the GCD of 55 and 132.

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 repeatedly apply this principle until the two numbers are equal, at which point we have found the GCD.

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 two numbers.

Let's apply the Euclidean algorithm to find the GCD of 55 and 132:

1. Divide 132 by 55: - 132 = 55 * 2 + 22

2. Divide 55 by 22: - 55 = 22 * 2 + 11

3. Divide 22 by 11: - 22 = 11 * 2 + 0

Since the remainder is 0, the GCD of 55 and 132 is 11.

Conclusion

The greatest common divisor (GCD) of 55 and 132 is 11. This result is obtained using the Euclidean algorithm, which involves iteratively finding the remainder of the division of the larger number by the smaller number until the remainder is 0