Prime Factorization (Medium)

Prime Factorization: core idea

• 1. Find $\gcd(84,126)$.

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• 2. Find $\operatorname{lcm}(45,60)$.

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• 3. How many perfect-square divisors does $360$ have?

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• 4. What is the least $n$ such that $72n$ is a perfect square?

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• 5. How many positive factors of $1000$ are multiples of $10$?

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• 6. Find the sum of the prime factors of $462$.

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• 7. What is the greatest square dividing $540$?

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• 8. How many divisors of $2^4\cdot3^3$ are divisible by $12$?

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• 9. Find the least positive integer with exactly $6$ positive divisors.

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