Questions: Find the greatest common divisor of the numbers. 16 and 18 The greatest common divisor of 16 and 18 is . (Type a whole number.)

Solution Steps

To find the greatest common divisor (GCD) of two numbers, we can use the Euclidean algorithm, which involves repeated division and taking remainders until the remainder is zero. The last non-zero remainder is the GCD.

We are given two numbers: \( a = 16 \) and \( b = 18 \).

To find the greatest common divisor (GCD) of \( a \) and \( b \), we use the Euclidean algorithm, which involves the following steps:

1. Divide \( a \) by \( b \) and find the remainder: \( 16 \div 18 = 0 \) remainder \( 16 \).
2. Replace \( a \) with \( b \) and \( b \) with the remainder: \( a = 18 \), \( b = 16 \).
3. Repeat the division: \( 18 \div 16 = 1 \) remainder \( 2 \).
4. Replace \( a \) with \( b \) and \( b \) with the remainder: \( a = 16 \), \( b = 2 \).
5. Repeat the division: \( 16 \div 2 = 8 \) remainder \( 0 \).

The process stops when the remainder is \( 0 \). The last non-zero remainder is the GCD. In this case, the GCD is \( 2 \).

Final Answer