Ready to unlock the mysteries of numbers? Our Ultimate Number Theory & Fractions Quiz is designed for curious minds eager to sharpen their skills and have fun with math. This number theory quiz guides you through a factors and multiples quiz section and rigorous prime factorization test puzzles, while the interactive fractions quiz challenges your ability to simplify, compare, and convert fractions flawlessly. Whether you're reviewing for class or love a good math trivia quiz, our free challenge will boost your problem-solving confidence. Dive into our Number Theory Quiz and tackle the fraction quiz now - let's see how high you can score!
What is the greatest common factor of 12 and 18?
6
3
12
18
The factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 18 are 1, 2, 3, 6, 9, 18. The largest number common to both lists is 6. This is known as the greatest common factor. Learn more.
Which of these fractions is equivalent to 1/2?
2/4
3/4
1/3
2/3
To see if a fraction is equivalent to 1/2, multiply numerator and denominator by the same number. 1×2/2×2 = 2/4. Thus 2/4 is equivalent to 1/2. Read more.
Which of the following is a prime number?
29
27
21
1
A prime number has exactly two distinct positive divisors: 1 and itself. 29 is divisible only by 1 and 29, so it is prime. Numbers like 27 and 21 have additional divisors. See details.
What is 3/5 + 1/5?
4/5
1/5
3/10
2/5
When adding fractions with the same denominator, add the numerators and keep the denominator. 3 + 1 = 4, so 3/5 + 1/5 = 4/5. More info.
Which number is a multiple of both 4 and 6?
12
18
8
14
A multiple of both 4 and 6 must be divisible by both. 12 ÷ 4 = 3 and 12 ÷ 6 = 2, so 12 is a common multiple. Learn more.
What is 7 ÷ 49 expressed as a fraction in simplest form?
1/7
7/49
1/49
7
Division 7 ÷ 49 can be written as the fraction 7/49. Simplify by dividing numerator and denominator by 7 to get 1/7. See how.
What is the least common multiple of 3 and 5?
15
8
10
5
Multiples of 3 are 3,6,9,12,15, and multiples of 5 are 5,10,15. The smallest common one is 15. Learn more.
Which of these is the reciprocal of 4/9?
9/4
4/9
1/9
1/4
The reciprocal of a fraction is obtained by swapping numerator and denominator. The reciprocal of 4/9 is 9/4. More details.
What is the greatest common factor of 24 and 36?
12
6
24
18
Factors of 24: 1,2,3,4,6,8,12,24; factors of 36:1,2,3,4,6,9,12,18,36. Largest common factor is 12. Read more.
What is 5/8 minus 1/4?
3/8
1/2
4/8
5/4
Convert 1/4 to eighths: 1/4 = 2/8, then subtract: 5/8 - 2/8 = 3/8. Learn more.
Convert the improper fraction 11/4 to a mixed number.
2 3/4
3 1/4
2 1/4
4 3/11
Divide 11 by 4: quotient is 2, remainder 3, so 11/4 = 2 3/4. See explanation.
Simplify the fraction 45/60.
3/4
4/5
45/60
5/6
Divide numerator and denominator by their GCF, 15: 45÷15=3 and 60÷15=4, so 45/60 simplifies to 3/4. Learn more.
What is the least common multiple of 4, 6, and 8?
24
12
48
16
Multiples of 8 include 8,16,24. Check if 24 is divisible by 4 and 6: 24÷4=6, 24÷6=4. So LCM is 24. More info.
Which of these fractions is equal to 0.75?
3/4
2/3
1/3
4/5
0.75 means 75 out of 100, which simplifies to 3/4 when dividing by 25. See conversion.
What is the prime factorization of 28?
2 × 2 × 7
2 × 14
4 × 7
28
28 = 2 × 14 and 14 = 2 × 7, so written as primes: 2 × 2 × 7. Learn more.
What are the prime factors of 91?
7 and 13
7 and 11
13 and 11
7 and 17
91 ÷ 7 = 13 with no remainder, so 7 and 13 are the prime factors of 91. More details.
What is the result of (2/3) × (9/4)?
3/2
18/12
1/6
9/8
Multiply numerators and denominators: (2×9)/(3×4)=18/12, which simplifies by dividing by 6 to get 3/2. Read more.
Which is larger: 7/11 or 2/3?
2/3
7/11
They are equal
Cannot compare
Convert to decimals: 7/11?0.636, 2/3?0.667. Since 0.667>0.636, 2/3 is larger. Learn how.
Simplify (5/6) ÷ (10/9).
3/4
9/12
5/54
6/5
Division by a fraction is multiply by its reciprocal: (5/6)×(9/10)=45/60 which simplifies to 3/4. More info.
What is the least common denominator for adding 3/4, 5/6, and 7/8?
24
48
12
16
Find LCM of denominators: LCM(4, 6, 8) = 24, so the least common denominator is 24. Learn more.
Find the greatest prime number less than 20.
19
17
18
13
Prime numbers under 20 are 2,3,5,7,11,13,17,19. The largest of these is 19. See list.
What is ?(9), Euler’s totient function of 9?
6
3
9
4
?(n) counts integers ?n that are coprime. For n=9, the coprime numbers are 1,2,4,5,7,8; total = 6. More on ?.
A fraction is 3/5 of a number; if the fraction equals 12, what is the number?
20
15
18
24
If (3/5)×x = 12, multiply both sides by 5/3: x = 12×(5/3) = 20. See how.
If a/b = 4/7 and b/c = 14/9, what is a/c?
8/9
4/9
56/63
7/9
a/c = (a/b)×(b/c) = (4/7)×(14/9) = 56/63 which simplifies to 8/9. Learn more.
What is the value of the infinite series 1/2 + 1/4 + 1/8 + ...?
1
2
Infinity
1/2
This is a geometric series with first term 1/2 and ratio 1/2. Sum = a/(1?r) = (1/2)/(1?1/2) = 1. See derivation.
Find the smallest positive integer n such that n ? 2 mod 3, n ? 3 mod 4, and n ? 1 mod 5.
11
7
17
23
By testing or using the Chinese remainder theorem, 11 mod 3 = 2, mod 4 = 3, mod 5 = 1. It is the smallest positive solution. More on CRT.
What is the highest power of 2 that divides 100!?
97
96
99
100
Use Legendre’s formula: ?100/2?+?100/4?+?100/8?+?100/16?+?100/32?+?100/64? = 50+25+12+6+3+1 = 97. Learn more.
How many trailing zeros does 1000! have?
249
248
252
250
Count factors of 5: ?1000/5?+?1000/25?+?1000/125?+?1000/625? = 200+40+8+1 = 249. Each factor of 5 pairs with a 2 to make a trailing zero. More info.
0
{"name":"What is the greatest common factor of 12 and 18?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the greatest common factor of 12 and 18?, Which of these fractions is equivalent to 1\/2?, Which of the following is a prime number?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}
Study Outcomes
Identify Prime and Composite Numbers -
Distinguish prime numbers from composite ones by evaluating divisibility rules and essential number theory concepts.
Analyze Factors and Multiples -
Determine all factors and multiples of given numbers, including greatest common factors and least common multiples, with confidence.
Apply Prime Factorization Techniques -
Use systematic methods to break down numbers into their prime factors, reinforcing skills tested in the prime factorization test.
Simplify and Compare Fractions -
Reduce fractions to simplest form and compare their values accurately, strengthening your foundation in the fractions quiz segment.
Solve Number Theory Challenges -
Employ strategic problem-solving approaches to tackle a variety of number theory quiz questions under time constraints.
Assess Math Proficiency -
Evaluate your overall performance through instant feedback on factors, multiples, prime numbers, and fractions, boosting your math confidence.
Cheat Sheet
Unique Prime Factorization -
The Fundamental Theorem of Arithmetic states every integer greater than 1 can be expressed uniquely as a product of primes, ignoring order. For example, 360 = 2³ × 3² × 5, and mastering this decomposition underpins proofs and problem solving in number theory (see MIT OpenCourseWare for reference).
Divisibility Rules for Quick Tests -
Memorize simple tests: a number is divisible by 3 if its digits sum to a multiple of 3, by 5 if it ends in 0 or 5, and by 7 using the "double-and-subtract" trick. These shortcuts speed up prime factorization and are reinforced in resources like Khan Academy.
GCD and LCM via Prime Powers -
Compute the Greatest Common Divisor by taking the minimum exponent of shared prime factors and the Least Common Multiple by taking the maximum exponent. For instance, for 18 (2 × 3²) and 24 (2³ × 3), GCD = 2¹ × 3¹ = 6 and LCM = 2³ × 3² = 72, as outlined in standard college algebra texts.
Fraction Simplification & Equivalent Forms -
Use prime factorization to cancel common factors in numerator and denominator, e.g., 28/36 = (2²×7)/(2²×3²) = 7/9. Recognize equivalence by multiplying or dividing both terms by the same nonzero integer, a technique emphasized in National Council of Teachers of Mathematics guidelines.
Converting and Comparing Fractions -
Transform improper fractions to mixed numbers (e.g., 11/4 = 2¾) and vice versa by division and recombination. Compare fractions by cross-multiplication - 3/8 vs. 2/5 becomes 3×5=15 vs. 2×8=16 - so 2/5 is larger, a strategy featured in university preparatory curricula.
