Find the greatest common divisor of -30 and 95.

Here's a step-by-step explanation to find the greatest common divisor of -30 and 95. Step 1: Verify that the numbers are integers Verify that the numbers -30 and 95 are both integers. Step 2: Make both numbers positive To ensure a non-negative result, make both numbers positive by taking their absolute values: |-30| = 30 and |95| = 95. Step 3: Now the problem is to find the GCD of 30 and 95 To find the GCD, we can use the Euclidean Algorithm, which is an efficient way of finding the GCD of two numbers. The algorithm is as follows: 1. If either of the numbers is zero, the GCD is the other number. 2. If both numbers are non-zero, divide the larger number by the smaller number, and replace the larger number with the remainder. 3. Repeat step 2 until the remainder is zero. Step 4: Apply the Euclidean Algorithm Now, perform the steps from the Euclidean Algorithm for the numbers 30 and 95. 1. Remainder of 95 divided by 30: $$\begin{gathered} 95 \\ div30=3 \\ :remainder5 \end{gathered}$$ 2. Remainder of 30 divided by 5: $$\begin{gathered} 30 \\ div5=6 \\ :remainder0 \end{gathered}$$ The remainder is now zero, so the GCD is the last non-zero remainder we obtained, which was 5. Step 5: State the GCD The greatest common divisor of -30 and 95 is 5.