Lesson 4: Prime Factorization — 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. A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Which of the following numbers is divisible by 4?

   • A. 3,114
   • B. 5,226
   • C. 8,438
   • D. 6,752

7. 7. What is the smallest single digit that can be placed in the blank to make the number 5,1_4 divisible by 9?

8. 8. A number is divisible by 6 if it is even and the sum of its digits is divisible by 3. Which of these numbers is divisible by 6?

   • A. 2,451
   • B. 3,142
   • C. 5,502
   • D. 6,113

9. 9. A number is divisible by 8 if the number formed by its last three digits is divisible by 8. Which of these numbers is divisible by 8?

   • A. 12,148
   • B. 34,218
   • C. 76,512
   • D. 51,342

10. 10. The number 7,110 is divisible by which of the following sets of numbers?

    • A. 3, 4, and 5
    • B. 2, 3, and 9
    • C. 5, 8, and 9
    • D. 4, 6, and 9