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Quizzes > High School Quizzes > Mathematics

Prime & Composite Practice Quiz

Sharpen math skills with fun number challenges

Difficulty: Moderate
Grade: Grade 5
Study OutcomesCheat Sheet
Paper art promoting Prime Composite Quest, a trivia quiz for middle school students mastering math concepts.

Which of the following best describes a prime number?
A number that is always even
A number with exactly two distinct positive factors, 1 and itself
A number that can be divided by any other number
A number with more than two factors
A prime number is defined as having exactly two distinct factors: 1 and the number itself. This excludes numbers that have additional divisors.
Which of these numbers is prime?
4
9
7
6
7 is a prime number because its only positive divisors are 1 and 7. The other numbers have additional factors that make them composite.
Which of the following numbers is composite?
11
15
13
17
15 is composite because it can be evenly divided by 3 and 5, in addition to 1 and 15. The other numbers are prime, having only two factors.
How many factors does a prime number have?
More than two factors
Exactly three factors
Only one factor
Exactly two factors
By definition, a prime number has exactly two factors: 1 and itself. This is the defining characteristic that distinguishes prime numbers from composites.
Which of the following statements indicates a composite number?
It is a prime number
It is always even
It has divisors other than 1 and itself
It is divisible only by 1 and itself
A composite number is one that has more than two factors, meaning it has divisors other than just 1 and itself. This property clearly distinguishes composite numbers from primes.
What is the smallest prime number?
1
2
0
3
The smallest prime number is 2 because it has exactly two factors: 1 and 2. The number 1 is not considered prime since it only has one factor.
Which number is the only even prime number?
4
8
6
2
2 is the only even prime number because every other even number can be divided by 2 and at least one other number, making them composite. This unique property makes 2 especially important in prime number theory.
Which of the following is the correct prime factorization of 30?
2 x 15
2 x 3 x 5
3 x 10
5 x 6
The number 30 breaks down into prime factors as 2, 3, and 5. This option correctly represents its factorization solely using prime numbers.
Which number is prime among the following options: 21, 23, 25, 27?
21
27
25
23
23 is prime because its only divisors are 1 and 23. The other numbers have additional factors, classifying them as composite.
Which of the following statements about composite numbers is true?
Composite numbers are only divisible by 1 and themselves
Composite numbers have more than two factors
Composite numbers are always odd
Composite numbers are numbers that come after primes
Composite numbers are identified by having more than two factors. This option correctly states the defining property of composite numbers.
If a number has exactly three factors, what type of number is it most likely to be?
A composite number with four factors
A prime number
An odd composite number
A perfect square of a prime number
A number with exactly three factors is typically the square of a prime, because its factors are 1, the prime number, and the square itself. This property is unique to such numbers.
What is the prime factorization of 18?
2 x 3 x 3
3 x 6
2 x 3
2 x 9
Breaking 18 into its prime factors yields 2 x 3 x 3. The other options either do not use only prime numbers or do not multiply to 18 correctly.
Which of the following numbers is composite and divisible by 3?
7
11
13
9
9 is composite because it factors into 3 x 3, showing divisibility by 3. The other numbers are prime and do not have additional factors.
Which of these numbers is composite?
17
2
3
25
25 is composite because it has a divisor other than 1 and itself (namely, 5). The other numbers listed are prime.
When you add a prime number to a composite number, the sum can be:
Either prime or composite depending on the numbers
Always composite
Always even
Always prime
The sum of a prime number and a composite number does not have a predictable outcome; it can be either prime or composite based on the specific values involved. This highlights the variability in number properties.
Determine the prime factorization of 84.
2 x 3 x 7
2 x 3 x 3 x 7
2 x 2 x 3 x 7
2 x 2 x 7
84 factors into prime numbers as 2 x 2 x 3 x 7. The other options either omit a necessary factor or include an extra one that does not correctly multiply to 84.
Which of the following lists contains only prime numbers?
2, 3, 6, 7
3, 5, 7, 9
2, 4, 5, 7
2, 3, 5, 7
The set {2, 3, 5, 7} contains only prime numbers, while the other lists include at least one composite number. Recognizing pure sets of primes is crucial to understanding number theory.
Which of the following numbers is composite even though it might seem prime at first glance?
37
29
49
41
Although 49 might appear prime at a quick glance, it is composite because it is 7 x 7. The other numbers are confirmed to be prime.
Which of the following composite numbers has distinct prime factors that add up to 10?
21
18
42
28
The number 21 has distinct prime factors 3 and 7, which sum to 10. The other numbers do not have sets of prime factors that satisfy this condition.
What is a necessary condition for a number to be considered composite?
It must be an odd number
It must be greater than 50
It must be a prime number
It must have more than two factors
A composite number is defined by having more than two factors; this means it must have divisors besides 1 and itself. This condition is fundamental in distinguishing composite numbers from primes.
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Study Outcomes

  1. Understand the defining characteristics of prime and composite numbers.
  2. Identify prime and composite numbers in various problem-solving scenarios.
  3. Apply factorization techniques to determine the factors of composite numbers.
  4. Analyze numerical patterns using the properties of prime and composite numbers.
  5. Synthesize learned concepts to solve math puzzles and prepare for exams confidently.

Prime and Composite Number Worksheet Cheat Sheet

  1. Identify Prime Numbers - A prime number is a natural number greater than 1 that has exactly two distinct positive factors: 1 and itself. It's like a number that shuns all divisors except its own twin and the lonely 1. Examples include 2, 3, 5, and 7, which refuse to be broken down further. Practice prime vs. composite
    2. onlinemathlearning.com
  2. Spot Composite Numbers - A composite number is a natural number greater than 1 that has more than two distinct positive factors, making it a bit more divisible than its prime pals. For instance, 4 splits into 1, 2, and 4, while 6 has 1, 2, 3, and 6. Recognizing composites helps you see the factor party happening behind the scenes. Test your composite skills
    3. onlinemathlearning.com
  3. The Special Case of 1 - The number 1 is neither prime nor composite because it only has one positive divisor: itself. It's the unique loner in the number world, sitting on its own. Remember to treat it as a solo act when classifying numbers. Learn more about number 1
    4. onlinemathlearning.com
  4. The Lone Even Prime - The number 2 is the only even prime because any other even number can be split by 2 and at least one other factor. This makes 2 the undefeated champion of primes. Embrace the uniqueness of 2 when you're hunting for even primes. Explore the even prime
    5. onlinemathlearning.com
  5. Use the Sieve of Eratosthenes - The Sieve of Eratosthenes is an ancient yet powerful algorithm for finding all primes up to a chosen number, plucking out multiples like a pro. You start at 2 and keep striking out every multiple until only primes remain. It's like a treasure hunt where you wash away the riff‑raff to reveal hidden gems! Try the sieve method
    6. onlinemathlearning.com
  6. Master Prime Factorization - Every whole number greater than 1 is either prime or can be broken down into prime factors, called prime factorization. For example, 12 can be expressed as 2 × 2 × 3, showing the building blocks of 12. This concept is crucial for simplifying fractions and understanding number structures. Factor like a champ
    7. onlinemathlearning.com
  7. Practice with Worksheets - Regular practice is your best friend when it comes to spotting prime and composite numbers quickly and accurately. Worksheets provide varied exercises that challenge and solidify your skills. Keep at it, and you'll gain confidence faster than you can say "prime!" Grab printable worksheets
    8. superteacherworksheets.com
  8. Discover Twin Primes - Twin primes are pairs of primes that only differ by 2, like 3 and 5 or 11 and 13, giving them a special bond. Finding twin primes is like spotting paired superheroes in the number universe. They add an extra layer of intrigue to your prime-number adventures. Dive into twin primes
    9. mathfunworksheets.com
  9. Understand Co-Primes - Co-prime, or relatively prime, numbers are pairs that share no common factors other than 1, such as 8 and 15. They're best buddies in the factoring world because their only shared divisor is the simple 1. Co‑prime relationships are key for reducing fractions and solving certain number puzzles. Study co-prime pairs
    10. mathfunworksheets.com
  10. Use Prime Charts - Visual charts listing prime numbers up to 100 can be a game changer, letting you quickly spot primes without re-computing factors. They're like a road map that steers you away from composite cul-de-sacs. Keep a chart handy to speed up your problem-solving and impress your peers. Download prime charts
    11. superteacherworksheets.com
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