provet of 350 and 5613 .

UpStudy ThothAI Solution

Tutor-Verified Answer

Step-by-step Solution

To find the greatest common divisor (GCD) of 350 and 5613, we can use the Euclidean algorithm. The steps are as follows: 1. Divide 5613 by 350 and find the remainder. 2. Replace 5613 with 350 and 350 with the remainder from step 1. 3. Repeat the process until the remainder is 0. The last non-zero remainder is the GCD. Let's perform the calculations: 1. \( 5613 \div 350 \) gives a quotient of 16 and a remainder of: \[ 5613 - (350 \times 16) = 5613 - 5600 = 13 \] 2. Now, replace 5613 with 350 and 350 with 13: \[ 350 \div 13 \text{ gives a quotient of } 26 \text{ and a remainder of: } \] \[ 350 - (13 \times 26) = 350 - 338 = 12 \] 3. Now, replace 350 with 13 and 13 with 12: \[ 13 \div 12 \text{ gives a quotient of } 1 \text{ and a remainder of: } \] \[ 13 - (12 \times 1) = 13 - 12 = 1 \] 4. Now, replace 13 with 12 and 12 with 1: \[ 12 \div 1 \text{ gives a quotient of } 12 \text{ and a remainder of: } \] \[ 12 - (1 \times 12) = 12 - 12 = 0 \] Since the last non-zero remainder is 1, the GCD of 350 and 5613 is **1**. This means that 350 and 5613 are coprime (they have no common factors other than 1).