Find the greatest common divisor of 84 and 126.

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Multiple Choice

Find the greatest common divisor of 84 and 126.

Explanation:
The greatest common divisor is the largest number that divides both numbers without a remainder.Factor each number: 84 = 2^2 × 3 × 7 and 126 = 2 × 3^2 × 7. The common prime factors with the smallest exponents are 2^1, 3^1, and 7^1, giving 2 × 3 × 7 = 42. So 42 divides both numbers (84 ÷ 42 = 2 and 126 ÷ 42 = 3), and no larger number can divide both. Another quick check with the Euclidean algorithm: 126 = 84 × 1 + 42, then 84 = 42 × 2 + 0, so the gcd is 42.

The greatest common divisor is the largest number that divides both numbers without a remainder.Factor each number: 84 = 2^2 × 3 × 7 and 126 = 2 × 3^2 × 7. The common prime factors with the smallest exponents are 2^1, 3^1, and 7^1, giving 2 × 3 × 7 = 42. So 42 divides both numbers (84 ÷ 42 = 2 and 126 ÷ 42 = 3), and no larger number can divide both. Another quick check with the Euclidean algorithm: 126 = 84 × 1 + 42, then 84 = 42 × 2 + 0, so the gcd is 42.

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