What is the greatest common divisor of 18 and 24?

What is the greatest common divisor of 18 and 24?

• A. 2
• B. 6
• C. 4
• D. 3

Answer: (B)

To determine the greatest common divisor (GCD) of 18 and 24, we start by finding the prime factorization of both numbers. For 18, the prime factorization is: - 18 = 2 × 3 × 3, or 2 × 3². For 24, the prime factorization is: - 24 = 2 × 2 × 2 × 3, or 2³ × 3. Next, we identify the common prime factors in both factorizations. The common prime factors are 2 and 3. To find the GCD, we take the lowest power of each common prime factor: - For the prime factor 2, the lowest power from both factorizations is 2¹ (from 18). - For the prime factor 3, the lowest power is 3¹ (which is present in both). Thus, we multiply these together to get the GCD: GCD = 2¹ × 3¹ = 2 × 3 = 6. This means the greatest common divisor of 18 and 24 is indeed 6, confirming that the correct answer is the option indicating 6. This result indicates the largest number

To determine the greatest common divisor (GCD) of 18 and 24, we start by finding the prime factorization of both numbers.

For 18, the prime factorization is:

• 18 = 2 × 3 × 3, or 2 × 3².

For 24, the prime factorization is:

• 24 = 2 × 2 × 2 × 3, or 2³ × 3.

Next, we identify the common prime factors in both factorizations. The common prime factors are 2 and 3. To find the GCD, we take the lowest power of each common prime factor:

• For the prime factor 2, the lowest power from both factorizations is 2¹ (from 18).

• For the prime factor 3, the lowest power is 3¹ (which is present in both).

Thus, we multiply these together to get the GCD:

GCD = 2¹ × 3¹ = 2 × 3 = 6.

This means the greatest common divisor of 18 and 24 is indeed 6, confirming that the correct answer is the option indicating 6. This result indicates the largest number