What is the greatest common divisor of 18 and 24?

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Multiple Choice

What is the greatest common divisor of 18 and 24?

The greatest common divisor is the largest number that divides both numbers evenly. To see what that is here, look at the factors of each number. The divisors of 18 are 1, 2, 3, 6, 9, and 18. The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The common divisors are 1, 2, 3, and 6, with 6 being the largest. So the greatest common divisor is 6. Another way to view it is by prime factorization: 18 = 2 × 3² and 24 = 2³ × 3. The shared prime factors are 2¹ and 3¹, giving 2 × 3 = 6. The other options don’t work because 12 doesn’t divide 18, 9 doesn’t divide 24, and 3 is smaller than the actual greatest common divisor.

The greatest common divisor is the largest number that divides both numbers evenly. To see what that is here, look at the factors of each number. The divisors of 18 are 1, 2, 3, 6, 9, and 18. The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The common divisors are 1, 2, 3, and 6, with 6 being the largest. So the greatest common divisor is 6.

Another way to view it is by prime factorization: 18 = 2 × 3² and 24 = 2³ × 3. The shared prime factors are 2¹ and 3¹, giving 2 × 3 = 6. The other options don’t work because 12 doesn’t divide 18, 9 doesn’t divide 24, and 3 is smaller than the actual greatest common divisor.

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