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Prime Factorization (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Prime Factorization: core idea

Factor small n.

Example problem: hint and answer

Find the prime factorization exponent of 22 in 7272.

Hint: Factor into primes, then use exponents. Answer: 3.

Practice (9 problems — type your answers)

  • 1. How many positive divisors does 3636 have?

  • 2. Find the greatest prime factor of 9191.

  • 3. What is gcd⁡(18,30)\gcd(18,30)?

  • 4. What is lcm⁡(8,12)\operatorname{lcm}(8,12)?

  • 5. How many distinct prime factors does 210210 have?

  • 6. Find the smallest prime factor of 143143.

  • 7. What is the product of the distinct prime factors of 6060?

  • 8. How many factors of 4848 are odd?

  • 9. Find the exponent of 33 in 243243.

Prime Factorization Practice Problems — Easy