What is the largest number that will divide both 45 and 60 perfectly, with no remainder?

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Multiple Choice

What is the largest number that will divide both 45 and 60 perfectly, with no remainder?

Explanation:
You're being asked to find the greatest number that can divide both 45 and 60 with no remainder—the greatest common divisor. Do the prime factorization: 45 = 3^2 × 5, and 60 = 2^2 × 3 × 5. The common prime factors are 3 and 5, and you take the smallest powers they share: 3^1 and 5^1. Multiply them together to get 3 × 5 = 15. So 15 can divide both numbers evenly: 45 ÷ 15 = 3 and 60 ÷ 15 = 4. No larger number can divide both at the same time, so 15 is the largest common divisor.

You're being asked to find the greatest number that can divide both 45 and 60 with no remainder—the greatest common divisor.

Do the prime factorization: 45 = 3^2 × 5, and 60 = 2^2 × 3 × 5. The common prime factors are 3 and 5, and you take the smallest powers they share: 3^1 and 5^1. Multiply them together to get 3 × 5 = 15. So 15 can divide both numbers evenly: 45 ÷ 15 = 3 and 60 ÷ 15 = 4.

No larger number can divide both at the same time, so 15 is the largest common divisor.

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