Question

Докажите что :числа380 и 399 не являются взаимно простыми

Answer 1

380/2/160/2/80/2/40/2/20/2/10/2/5/5/1
399/3/133/7/19/19/1
НОД=1

Answer 2

Introduction

To prove that the numbers 380 and 399 are not coprime (or mutually prime), we need to show that they have a common divisor other than 1. In other words, if there exists a positive integer greater than 1 that divides both 380 and 399, then the numbers are not coprime.

Proof

To determine if 380 and 399 have a common divisor, we can calculate their greatest common divisor (GCD) using the Euclidean algorithm. The Euclidean algorithm states that the GCD of two numbers can be found by repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero.

Let's calculate the GCD of 380 and 399:

1. Divide 399 by 380: 399 ÷ 380 = 1 with a remainder of 19. 2. Divide 380 by 19: 380 ÷ 19 = 20 with a remainder of 0.

Since the remainder is zero, the GCD of 380 and 399 is 19.

Conclusion

The GCD of 380 and 399 is 19, which is greater than 1. Therefore, we have proven that the numbers 380 and 399 are not coprime or mutually prime.