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Quizzes > High School Quizzes > Mathematics

Greatest Common Factor Worksheets Practice Quiz

Master factoring techniques with engaging worksheet challenges

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting GCF Factor Frenzy, an engaging math quiz for middle school students.

What is the greatest common factor of 8 and 12?
2
4
8
6
The factors of 8 are 1, 2, 4, and 8, and the factors of 12 are 1, 2, 3, 4, 6, and 12. The largest common factor between the two is 4.
Which of the following is the greatest common factor of 9 and 15?
15
5
9
3
The factors of 9 are 1, 3, and 9, while the factors of 15 are 1, 3, 5, and 15. Therefore, the greatest common factor is 3.
Find the greatest common factor of 5 and 20.
20
10
15
5
The number 5 has factors 1 and 5, and 20 has factors 1, 2, 4, 5, 10, and 20. The highest factor they share is 5.
What is the greatest common factor of 14 and 21?
14
21
3
7
For 14, the factors are 1, 2, 7, and 14, and for 21 they are 1, 3, 7, and 21. The largest common factor is 7.
Determine the greatest common factor of 10 and 15.
5
2
15
10
The factors of 10 are 1, 2, 5, and 10, while those of 15 are 1, 3, 5, and 15. This means the greatest common factor is 5.
What is the greatest common factor of 24 and 36?
12
18
6
8
The factors of 24 include 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, and 36. The largest common factor between the two numbers is 12.
What is the greatest common factor of 42 and 56?
14
28
21
7
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42, and the factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. The greatest common factor they share is 14.
Determine the greatest common factor of 18, 24, and 30.
3
2
12
6
Using prime factorization: 18 = 2 � - 3², 24 = 2³ � - 3, and 30 = 2 � - 3 � - 5. The common factors are 2 and 3, which multiply to give a GCF of 6.
Which method is most efficient for finding the GCF of large numbers?
Euclidean algorithm
Multiplying the numbers
Prime factorization
Listing all factors
While listing factors and prime factorization can be effective for smaller numbers, the Euclidean algorithm is much more efficient for larger numbers. It reduces the problem by repeatedly using division.
Find the GCF of 60 and 90.
15
45
60
30
The prime factorization of 60 is 2² � - 3 � - 5 and that of 90 is 2 � - 3² � - 5. The common prime factors 2, 3, and 5 yield a GCF of 2 � - 3 � - 5 = 30.
What is the greatest common factor of 27 and 36?
6
12
9
3
The number 27 factors into 3³ while 36 factors into 2² � - 3². The highest power of 3 common to both numbers is 3², which is equal to 9.
Determine the GCF of 48 and 180.
12
6
18
24
The prime factorization of 48 is 2❴ � - 3, and 180 factors as 2² � - 3² � - 5. Taking the lowest power of common primes (2² and 3) gives 12, which is the GCF.
Find the GCF of 36, 60, and 84.
18
24
12
6
Breaking the numbers into their prime factors: 36 = 2² � - 3², 60 = 2² � - 3 � - 5, and 84 = 2² � - 3 � - 7. The common factors yield a GCF of 2² � - 3 = 12.
Which of the following represents the GCF of 16 and 28 using prime factorization?
7
8
4
2
Prime factorization gives 16 = 2❴ and 28 = 2² � - 7. The highest power of 2 common to both is 2², which equals 4, making it the GCF.
What is the term for two numbers that have a greatest common factor of 1?
Factors
Multiples
Composite
Relatively prime
If two numbers have a GCF of 1, they do not share any prime factors. Such numbers are described as 'relatively prime' or 'co-prime'.
Find the GCF of 100 and 85.
17
4
10
5
The prime factorization of 100 is 2² � - 5², while 85 factors into 5 � - 17. The only common prime factor is 5, making it the greatest common factor.
What is the greatest common factor of 32 and 48?
24
32
16
8
The number 32 is 2❵ and 48 is 2❴ � - 3. The largest common power of 2 is 2❴, which equals 16, making it the GCF.
Determine the GCF of 7 and 13.
91
7
13
1
Both 7 and 13 are prime numbers and do not share any common factors other than 1. Therefore, the GCF of 7 and 13 is 1.
Calculate the GCF of 81 and 54.
27
18
54
9
The prime factorization of 81 is 3❴, and 54 breaks down to 2 � - 3³. The common factor is 3³, which equals 27, making it the greatest common factor.
For the numbers 22 and 121, what is their greatest common factor?
2
11
22
1
The number 22 factors into 2 � - 11, and 121 is 11². The only common prime factor is 11, so the GCF of 22 and 121 is 11.
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5
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9
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11
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Study Outcomes

  1. Identify the greatest common factor of two or more numbers.
  2. Analyze prime factorizations to determine common factors.
  3. Apply strategies to simplify fractions using the greatest common factor.
  4. Synthesize steps to solve problems involving multiple factors.
  5. Evaluate the effectiveness of various approaches to finding the GCF in different scenarios.

Greatest Common Factor Worksheets Cheat Sheet

  1. Grasp the concept of GCF - The greatest common factor is the biggest number that divides two or more numbers evenly, leaving no leftovers. Think of it as the largest puzzle piece that fits perfectly into every number's jigsaw. Mastering this idea sets you up for smoother problem‑solving in math class. K5 Learning
  2. List out all factors - Write down every number that divides evenly into your given values, then spot the largest one they share. This hands‑on method helps you visualize how factors work together - and it's surprisingly satisfying when you circle that top common factor. It's a simple strategy you can use anytime. Chili Math
  3. Use prime factorization - Break each number down into primes (like 2, 3, 5, 7) and then pick the primes they have in common. Multiply those shared primes to get the GCF. This approach is like detective work - hunt for matching prime "clues" to crack the case. Online Math Learning
  4. Simplify fractions with GCF - To shrink a fraction, divide the numerator and the denominator by their GCF. You'll see your fraction transform into a simpler form, making calculations and comparisons way easier. It's a quick trick that fans out in algebra, science, and real‑world scenarios. Mathcation
  5. Spot GCF in ratios and proportions - Ratios and proportions often hide common factors begging to be simplified. Pulling out the GCF sharpens your ratios, making them clearer and more precise. Whether you're mixing paint or analyzing data, this skill keeps your numbers neat. NCTM Article
  6. Connect GCF to LCM - For any two numbers, the GCF multiplied by their least common multiple equals the product of the numbers themselves. This neat relationship ties together two key concepts in number theory. Once you see it in action, you'll marvel at math's hidden symmetry! NCTM Article
  7. Find GCF of monomials - When variables join the party, look at coefficients and variable powers separately to pick out common factors. For example, in 12x²y and 18xy², the GCF is 6xy. This skill powers up your algebra toolbox for simplifying expressions. Symbolab Guide
  8. Factor polynomials using GCF - Pull out the GCF from each term of a polynomial and rewrite it as a product, such as factoring 6x² + 9x into 3x(2x + 3). This step is the gateway to more advanced factoring techniques like grouping and quadratic formulas. You'll feel like a math magician! Symbolab Guide
  9. Recognize relatively prime pairs - If two numbers have a GCF of 1, they're called relatively prime, meaning they share no common factors except 1. This concept pops up in number theory and cryptography, where "co‑prime" relationships are key. It's a small fact with big implications! Chili Math
  10. Reinforce with practice - Drill your skills with worksheets, online quizzes, and real‑world problems to build confidence and speed. The more you practice, the faster you'll spot common factors in any math scenario. Keep at it and watch your GCF mastery skyrocket! MathBits Notebook
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