Chapter 3Prime Number

Prime Factorization Skills Lab

A focused quiz to practice breaking numbers into prime factors and applying them to GCD, LCM, and divisor problems.

15 questions
15 minutes

Practice Exercise

Chapter 3 Prime Number: Prime Factorization Skills Lab

Build confidence with the building blocks behind every integer. Practice decomposing numbers into their prime factors, analyze powers of primes, and apply factorization to compute greatest common divisors, least common multiples, and divisor counts. Through scaffolded exercises, gain fluency in translating between numbers and their prime power representations.

Learning Objectives for This Chapter

In this chapter, you'll develop mastery through carefully structured practice. Each objective builds upon the previous one, ensuring you gain both theoretical understanding and practical problem-solving skills.

Break composite numbers into prime factors efficiently using multiple strategies.

Interpret and manipulate prime power notation to answer quantitative questions.

Apply prime factorization to solve problems involving GCD, LCM, and divisor analysis.

Recommended related tools

These interactive tools are specially designed to complement your learning experience. Use them alongside this exercise to visualize concepts, explore patterns, and deepen your understanding through hands-on practice. Each tool provides unique insights that will enhance your problem-solving skills.

Prime Factorization Visualization Prime Number Explorer

Practice Questions

Answer all 25 questions below, then click "Check Answers" to see your results.

1
Which prime factorization equals 84?
84
2
The prime factorization below corresponds to which number?
2^3 \cdot 5
3
When factoring 540 completely into primes, what power of 3 appears?
540
4
Which option shows the correct prime factorization of 225?
225
5
Using prime factors, what is the greatest common divisor of 72 and 90?
\gcd(72, 90)
6
Which product of primes equals 231?
231
7
What is the prime factorization of 96?
96
8
Which number has exactly three distinct prime factors?
9
If a number n has the prime factorization shown, how many positive divisors does it have?
n = 2^4 \cdot 3^2 \cdot 5
10
What is the least common multiple of 18 and 24 when computed from their prime factorizations?
\operatorname{lcm}(18, 24)
11
Which integer results from evaluating the following expression?
2^2 \cdot 3 \cdot 11
12
Which statement illustrates the Fundamental Theorem of Arithmetic?
13
Which pair of numbers is relatively prime based on their prime factorizations?
14
What is the highest power of 2 dividing 144?
144
15
Which expression reconstructs 360 from prime powers?
360
16
Which number has the prime factorization shown below?
3^2 \cdot 5^2
17
What is the prime factorization of 128?
128
18
Which number is represented by the prime factorization 2^2 · 3 · 7?
2^2 \cdot 3 \cdot 7
19
How many prime factors (counting multiplicity) does 72 have?
72
20
Which expression gives the number of divisors of 180?
180 = 2^2 \cdot 3^2 \cdot 5
21
Which number equals 2^2 · 3^3 · 5?
2^2 \cdot 3^3 \cdot 5
22
Which statement about 101 is true?
101
23
Which product of primes equals 420?
420
24
If n = 2^3 · 3^2, what is n?
2^3 \cdot 3^2
25
Which number’s prime factorization includes exactly two distinct primes?
Share this chapter:
Previous
Identifying Prime and Composite Numbers
Next
Patterns and Properties of Primes

Related Series

Discussion (0)

U
Be respectful and constructive

No comments yet

Be the first to share your thoughts!