What is the greatest common factor of 48 and 180?

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Multiple Choice

What is the greatest common factor of 48 and 180?

Explanation:
The greatest common factor is the largest number that divides both numbers exactly. To find it, break each number down into prime factors: 48 = 2^4 × 3 and 180 = 2^2 × 3^2 × 5. The common primes are 2 and 3, so take the smallest powers that appear in both: 2^min(4,2) = 2^2 and 3^min(1,2) = 3^1. Multiply them together: 2^2 × 3 = 4 × 3 = 12. So the greatest common factor is 12, which means 12 divides both numbers. For context, 18 doesn’t divide 48, and 24 doesn’t divide 180, so they aren’t common factors as large as 12.

The greatest common factor is the largest number that divides both numbers exactly. To find it, break each number down into prime factors: 48 = 2^4 × 3 and 180 = 2^2 × 3^2 × 5. The common primes are 2 and 3, so take the smallest powers that appear in both: 2^min(4,2) = 2^2 and 3^min(1,2) = 3^1. Multiply them together: 2^2 × 3 = 4 × 3 = 12. So the greatest common factor is 12, which means 12 divides both numbers. For context, 18 doesn’t divide 48, and 24 doesn’t divide 180, so they aren’t common factors as large as 12.

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