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Quizzes > Mathematics

Factor Quiz: Practice Factors and Multiples

Quick, free multiples quiz to check your skills. Instant results.

Editorial: Review CompletedCreated By: Kendall BarnesUpdated Aug 24, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration of factors multiples quiz graphic with numbers and math symbols on golden yellow background

This quiz helps you practice factors and multiples, including prime factors, common multiples, and factor pairs. Check your answers instantly, then build speed with a multiplication fluency quiz and refresh facts in a multiplication table quiz. For broader review, try a basic math quiz today.

Which of these numbers is a factor of 18?
3
2
5
7
A factor of a number divides it evenly without leaving a remainder. Since 18 ÷ 3 = 6 exactly, 3 is a factor of 18. The other options do not divide 18 evenly. For more details, see .
Which of the following is not a multiple of 5?
22
10
15
25
A multiple of 5 ends in 0 or 5 when written in base 10. Since 22 ends in 2 and 22 ÷ 5 = 4.4, it is not a multiple of 5. The other choices all end in 0 or 5. Learn more at .
What is the greatest common factor of 12 and 18?
3
9
12
6
The greatest common factor (GCF) is the largest integer that divides both numbers. Both 12 and 18 are divisible by 6, and there is no larger common divisor. Thus, the GCF is 6. More at .
What is the least common multiple of 3 and 4?
7
12
3
6
The least common multiple (LCM) is the smallest number both originals divide into evenly. The multiples of 3 are 3, 6, 9, 12, and of 4 are 4, 8, 12. The first common number is 12. See .
What is the prime factorization of 84?
2^2 × 3 × 5
2^2 × 3 × 7
2^3 × 3 × 7
2 × 3^2 × 7
To find prime factors, divide by the smallest primes: 84 ÷ 2 = 42, 42 ÷ 2 = 21, 21 ÷ 3 = 7, and 7 is prime. This yields 2² × 3 × 7. For more, visit .
How many positive factors does 72 have?
12
8
18
6
First express 72 as prime factors: 2³ × 3². The total number of factors is (3+1)×(2+1) = 4×3 = 12. Each exponent plus one multiplied gives the count of divisors. See .
What is the least common multiple of 5, 10, and 15?
60
15
45
30
LCM of multiple numbers can be found pairwise: LCM of 5 and 10 is 10, then LCM of 10 and 15 is 30. Thus the smallest number divisible by all three is 30. More at .
Which two numbers are relatively prime?
14 and 21
8 and 12
9 and 27
15 and 28
Relatively prime numbers share no common prime factors, so their GCF is 1. The gcd of 15 and 28 is 1, making them relatively prime. The other pairs have larger common divisors. For details see .
If two numbers a and b have a GCF of 6 and an LCM of 180, and a = 30, what is b?
30
36
54
45
The relationship a × b = GCF(a,b) × LCM(a,b) holds. Plugging in gives 30 × b = 6 × 180, so b = (6 × 180) ÷ 30 = 36. See .
How many trailing zeros does 100! have when expressed in base 10?
25
22
20
24
Trailing zeros come from factors of 10, i.e., pairs of 2 and 5. Count the number of 5s: ?100/5? + ?100/25? = 20 + 4 = 24. Therefore, 100! ends in 24 zeros. More at .
A positive integer is divisible by both 8 and 9. Which of the following could it be?
48
72
54
36
A number divisible by both 8 and 9 must be a multiple of their LCM, which is 72. Among the options, only 72 meets that condition. See .
How many positive integers less than 50 are relatively prime to 50?
25
30
10
20
Use Euler's totient function ?(n) for n=50: 50×(1 - 1/2)×(1 - 1/5) = 50×1/2×4/5 = 20. There are 20 numbers less than 50 that are coprime to 50. Learn more at Euler's totient function.
What is the sum of all positive integer factors of 360 that are not multiples of 3?
120
45
180
90
First list factors of 360 with no factor of 3: they are of the form 2^a×5^b for a=0..3, b=0..1. Those eight factors sum to 1+2+4+8+5+10+20+40 = 90. For filtering factors, see .
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Study Outcomes

  1. Identify Factors -

    Identify and list all positive factors of a number to build a solid foundation for solving questions about factors.

  2. Determine Multiples -

    Calculate multiples of integers efficiently, sharpening your skills with this multiples trivia quiz.

  3. Differentiate Prime and Composite Numbers -

    Distinguish between prime and composite numbers when working through math factors quiz questions.

  4. Apply GCF and LCM Strategies -

    Compute the greatest common factor and least common multiple to tackle advanced factor and multiples quiz problems.

  5. Solve Real-World Number Problems -

    Use factors and multiples concepts to approach practical scenarios, enhancing problem-solving confidence.

  6. Evaluate Your Progress -

    Assess your understanding with immediate feedback, tracking growth through our basic math quiz format.

Cheat Sheet

  1. Prime Factorization Basics -

    Prime factorization breaks down any integer into its prime building blocks, as guaranteed by the Fundamental Theorem of Arithmetic (source: University Math Departments). For example, 84 = 2² × 3 × 7, which helps with many questions about factors and simplifies fraction work. Try the "factor tree" method: it's a fun visual tool to nail prime factors fast!

  2. Distinguishing Factors from Multiples -

    Factors divide a number evenly, while multiples are results of multiplying that number by an integer (MathisFun, 2024). For instance, factors of 12 are 1,2,3,4,6,12 and its first five multiples are 12,24,36,48,60 - crucial for any factors and multiples quiz. Remember: "If it fits, it's a factor; if it grows, it's a multiple!"

  3. GCF and LCM Strategies -

    Use the Euclidean algorithm to find the greatest common factor (GCF) quickly (source: MIT OpenCourseWare) and the formula GCF × LCM = product of the numbers to get the least common multiple. For example, for 18 and 24, GCF is 6, and LCM = (18×24)/6 = 72, a must-know trick for any multiples trivia quiz. This link between GCF and LCM unlocks many basic math quiz problems instantly.

  4. Key Divisibility Rules -

    Memorize simple rules for 2, 3, 5, and 9 to accelerate factor-finding (National Council of Teachers of Mathematics). A quick mnemonic: "Even guys don't cry" reminds you that even numbers (2), guys sum of digits (3), don't end in 5 or 0 (5), and digits sum to a multiple of 9 (9). Mastering these makes any math factors quiz feel like a breeze!

  5. Real-World Applications -

    Understanding factors and multiples powers up tasks like scheduling (LCM for event planning), simplifying recipes (GCF for ingredient ratios), and even cryptography (prime factors in RSA encryption). Practical examples - from calendar syncing to music rhythm patterns - show how these concepts solve everyday puzzles (source: Journal of Applied Mathematics). Embrace these applications to boost confidence before tackling your factors and multiples quiz!

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