What is the greatest common divisor (GCD) of 18 and 24?

To find the greatest common divisor (GCD) of 18 and 24, we can first determine the prime factorizations of both numbers.

The number 18 can be factored into primes as follows: 18 = 2 × 3 × 3 (or 2 × 3²).

For the number 24, the prime factorization is: 24 = 2 × 2 × 2 × 3 (or 2³ × 3).

Next, we identify the common prime factors between the two factorizations. Both numbers share the prime factors of 2 and 3.

Now, we take the smallest power of each common prime factor:

• For the prime factor 2, the smallest power in both factorizations is 2¹ (which appears in 18).
• For the prime factor 3, the smallest power is 3¹ (which appears in 18 as well).

Now, we multiply these together to find the GCD: GCD = 2¹ × 3¹ = 2 × 3 = 6.

Therefore, the greatest common divisor of 18 and 24 is 6, making it the correct answer. Understanding the prime factorization