Lesson 2: Prime Factorization and Special Factors — Practice Questions

1. 1. The prime factorization of a number is $2^2 \cdot 3^2 \cdot 5^1$. What is the largest perfect square factor of this number? ___

2. 2. Which number, given by its prime factorization, has a largest perfect square factor of $100$?

   • A. $2^3 \cdot 5^2 \cdot 7^1$
   • B. $2^1 \cdot 5^3 \cdot 7^1$
   • C. $2^2 \cdot 5^1 \cdot 7^2$
   • D. $2^4 \cdot 5^1 \cdot 7^1$

3. 3. The prime factorization of 54 is $2^1 \cdot 3^3$. What is the largest perfect square that is a factor of 54? ___

4. 4. The number 42 has a prime factorization of $2 \cdot 3 \cdot 7$. What is the largest perfect square factor of 42?

   • A. 1
   • B. 2
   • C. 4
   • D. 42

5. 5. A number has the prime factorization $2^5 \cdot 3^4 \cdot 5^1$. What is the largest perfect square factor of this number? ___

6. 6. The prime factorization of $144$ is ___. Use exponential notation.

7. 7. Find the prime factorization of $350$. The factorization is ___.

8. 8. What is the prime factorization of $525$? Express your answer using exponents for repeated factors. ___

9. 9. Using the factor tree method, find the prime factorization of 48. Express your answer using exponents. ___