Number Theory Trivia
Number Theory trivia explores the integers, prime numbers, divisibility, and surprising patterns that have fascinated mathematicians since antiquity, from Euclid to modern cryptography. This page offers a concise, family-friendly way to test what you know, whether you enjoy light number puzzles, odd mathematical facts, or more challenging questions about a foundational branch of mathematics.
Easy Number Theory Trivia
13 questions
These easy Number Theory trivia questions are great for beginners and kids around age 12 and under.
Question 1
What do you call a number with exactly two positive divisors, 1 and itself?
Answer: A prime number
A prime number is defined is having exactly two positive divisors: 1 and itself.
Question 2
A number with more than two positive divisors is called what?
Answer: A composite number
A composite number has more than two positive divisors.
Question 3
What is the smallest prime number?
- A.1
- B.3
- C.5
- D.2
Answer: 2
The smallest prime number is 2.
Question 4
Which number is neither prime nor composite?
- A.3
- B.1
- C.0
- D.2
Answer: 1
The number 1 is neither prime nor composite.
Question 5
What is the term for a number that equals the sum of its proper positive divisors?
Answer: A perfect number
A perfect number equals the sum of its proper positive divisors.
Question 6
What is the smallest perfect number?
- A.6
- B.4
- C.8
- D.12
Answer: 6
The smallest perfect number is 6.
Question 7
What do you call a number that reads the same forward and backward?
Answer: A palindromic number
A palindromic number reads the same forward and backward.
Question 8
Which of these is a palindromic number?
- A.11
- B.12
- C.10
- D.13
Answer: 11
11 reads the same forward and backward, so it is palindromic.
Question 9
A Mersenne prime has which general form?
Answer: 2^p - 1 for some prime p
A Mersenne prime has the form 2^p - 1, where p is prime.
Question 10
A Fermat number is written in what form?
Answer: 2^(2^n) + 1
A Fermat number has the form 2^(2^n) + 1.
Question 11
The Sophie Germain prime is named after which mathematician?
Answer: Sophie Germain
A Sophie Germain prime is named for Sophie Germain.
Question 12
Who proved that there are infinitely many prime numbers?
Answer: Euclid
Euclid proved that there are infinitely many prime numbers.
Question 13
What theorem describes how primes are distributed among large integers?
Answer: The prime number theorem
The prime number theorem describes the distribution of primes among large integers.
Number Theory Family Trivia
12 questions
These family Number Theory trivia questions are built for mixed-age game nights, classrooms, and groups.
Question 1
Which three single-digit numbers in this set are all prime numbers?
Answer: 3, 5, and 7
3, 5, and 7 are all prime numbers.
Question 2
Which number is composite because it can be written as 3 × 3?
- A.12
- B.9
- C.6
- D.8
Answer: 9
9 is composite because 9 = 3 × 3.
Question 3
What number has exactly four positive divisors: 1, 2, 5, and itself?
Answer: 10
10 has exactly four positive divisors: 1, 2, 5, and 10.
Question 4
Which number is divisible by both 3 and 4?
- A.14
- B.15
- C.12
- D.10
Answer: 12
12 is divisible by both 3 and 4.
Question 5
If you multiply 3 by 5, which number do you get?
Answer: 15
15 factors is 3 × 5, so 3 × 5 = 15.
Question 6
Which number has the factor pair 3 and 7?
- A.21
- B.18
- C.24
- D.27
Answer: 21
21 factors is 3 × 7.
Question 7
What number is the square of the prime number 5?
Answer: 25
25 is the square of the prime number 5.
Question 8
Which number equals 3 to the third power, or 3^3?
- A.18
- B.81
- C.27
- D.9
Answer: 27
27 is a power of 3, specifically 3^3.
Question 9
Which number is a Mersenne prime because it equals 2^5 - 1?
Answer: 31
31 is a Mersenne prime since 31 = 2^5 - 1.
Question 10
What are the smallest pair of amicable numbers?
Answer: 220 and 284
220 and 284 form the smallest pair of amicable numbers.
Question 11
Which number factors as 7 × 11 × 13?
Answer: 1001
1001 factors is 7 × 11 × 13.
Question 12
Which number is a palindromic prime?
- A.100
- B.111
- C.121
- D.101
Answer: 101
101 is a palindromic prime.
Fun Number Theory Trivia
13 questions
These fun Number Theory trivia questions highlight surprising moments and playful facts for game-night groups.
Question 1
Which Fibonacci number is also a prime, giving it a double life in two famous number families?
Answer: 13
13 appears in the Fibonacci sequence, and it is also prime.
Question 2
What number manages to be both a Fibonacci number and a perfect square?
Answer: 144
144 is a Fibonacci number, and it is also 12 squared.
Question 3
Which number is an Armstrong number because 1^3 + 5^3 + 3^3 equals the number itself?
Answer: 153
For 153, the sum of the cubes of its digits is 1 + 125 + 27 = 153.
Question 4
What is the smallest number that can be written as a sum of two cubes in two different ways?
Answer: 1729
1729 is the smallest number with two different representations is a sum of two cubes.
Question 5
Which pair of cube sums equals 1729?
- A.1^3 + 12^3 and 9^3 + 10^3
- B.2^3 + 12^3 and 8^3 + 11^3
- C.1^3 + 10^3 and 9^3 + 12^3
- D.4^3 + 11^3 and 6^3 + 9^3
Answer: 1^3 + 12^3 and 9^3 + 10^3
1729 has the two cube decompositions 1^3 + 12^3 and 9^3 + 10^3.
Question 6
If 1729 were bragging at a party, what special claim could it make?
- A.It is the smallest Carmichael number.
- B.It is a Fermat prime.
- C.It is both a Fibonacci number and a square.
- D.Smallest number expressible as two cubes
Answer: It is the smallest number expressible as the sum of two cubes in two different ways.
That special claim belongs to 1729.
Question 7
Which number is the smallest Carmichael number?
Answer: 561
561 is the smallest Carmichael number.
Question 8
What divisor sneaks into the Fermat number 2^32 + 1?
Answer: 641
641 divides the Fermat number 2^32 + 1.
Question 9
Which of these is a Fermat prime?
- A.641
- B.5040
- C.561
- D.65537
Answer: 65537
65537 is a Fermat prime.
Question 10
When 6 and 8 try to share nicely, what least common multiple do they agree on?
Answer: 24
The least common multiple of 6 and 8 is 24.
Question 11
What is the value of 7!, the factorial that grows from 7 all the way down to 1?
Answer: 5040
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
Question 12
In base 2, how is the decimal number 10 written?
Answer: 1010
The decimal number 10 is represented is 1010 in base 2.
Question 13
Which number on this list is a Fibonacci number: 92, 93, 94, or 95?
- A.95
- B.93
- C.92
- D.94
Answer: 93
93 is a Fibonacci number.
Funny Number Theory Trivia
13 questions
These funny Number Theory trivia questions highlight playful moments, odd facts, and inside jokes.
Question 1
Which number can honestly say, "I’m even," despite bringing absolutely no quantity to the party?
- A.1
- B.2
- C.3
- D.0
Answer: 0
Zero is even because it is divisible by 2.
Question 2
What three-digit number is divisible by 3, as if all those 1s decided to cooperate?
- A.111
- B.112
- C.110
- D.101
Answer: 111
111 is divisible by 3.
Question 3
Which number is just 11 squared wearing a tidy little disguise?
- A.101
- B.121
- C.111
- D.144
Answer: 121
121 equals 11^2.
Question 4
Which number is divisible by 2, 3, and 6, basically overachieving in three categories at once?
- A.223
- B.225
- C.222
- D.221
Answer: 222
222 is divisible by 2, 3, and 6.
Question 5
What number equals 7 cubed, like a lucky number getting promoted to the third dimension?
- A.343
- B.333
- C.441
- D.240
Answer: 343
343 equals 7^3.
Question 6
Which number is exactly 10 to the third power, with zeros doing most of the visual heavy lifting?
- A.2004
- B.1000
- C.1984
- D.1994
Answer: 1000
1000 equals 10^3.
Question 7
Which number reads the same forward and backward, making it the numerical equivalent of a mirror selfie?
- A.11000
- B.10001
- C.10010
- D.10100
Answer: 10001
10001 is a palindromic number.
Question 8
What palindrome looks like it hired a 2 to stand proudly in the middle?
- A.13231
- B.12321
- C.12345
- D.12231
Answer: 12321
12321 is a palindrome.
Question 9
In the multiplication 37 × 3, what number pops out like a very repetitive jackpot?
- A.121
- B.111
- C.107
- D.114
Answer: 111
37 × 3 = 111.
Question 10
Which square number is produced by 33 × 33, with perfect symmetry and no drama?
- A.1024
- B.1098
- C.9801
- D.1089
Answer: 1089
1089 is a square because 33^2 = 1089.
Question 11
The repeating decimal 0.142857... belongs to which fraction, patiently looping forever?
- A.2/7
- B.1/7
- C.1/3
- D.1/9
Answer: 1/7
0.142857 repeating is the decimal expansion of 1/7.
Question 12
Which six-digit number is identified here as a cyclic number in base 10, basically spinning its digits like a DJ?
- A.123456
- B.111111
- C.285714
- D.142857
Answer: 142857
142857 is a cyclic number in base 10.
Question 13
Which number shows up with exactly six zeros, as if it brought an entourage made entirely of nothing?
- A.1000
- B.1000000
- C.100000
- D.10000000
Answer: 1000000
1000000 has six zeros.
Hard Number Theory Trivia
14 questions
These hard Number Theory trivia questions are for expert fans who want a real challenge.
Question 1
In what year did Bernhard Riemann publish the paper that introduced his prime-counting ideas?
Answer: 1859
Bernhard Riemann published his paper on prime-counting ideas in 1859.
Question 2
Which year marks David Hilbert's presentation of his famous list of problems, including ones connected to number theory?
- A.1931
- B.2010
- C.1900
- D.1859
Answer: 1900
Hilbert presented his famous list of problems in 1900.
Question 3
Name the mathematician who proved the incompleteness theorems in 1931.?
Answer: Kurt Gödel
Kurt Gödel is proving the incompleteness theorems in 1931.
Question 4
What major international mathematics prize did John Tate win in 2010?
Answer: Abel Prize
John Tate won the Abel Prize in 2010, and separately notes that the Abel Prize is a major international mathematics prize.
Question 5
Which mathematician won the Abel Prize in 2003?
Answer: Pierre Serre
Pierre Serre won the Abel Prize in 2003.
Question 6
Who was awarded the Fields Medal in 2014 and is listed here as a notable modern figure in number theory?
Answer: Manjul Bhargava
Manjul Bhargava won the Fields Medal in 2014.
Question 7
Whose influence on modern algebraic geometry is singled out as deeply important for tools used in number theory?
Answer: Alexander Grothendieck
Alexander Grothendieck deeply influenced modern algebraic geometry used in number theory.
Question 8
Which mathematician's algebraic ideas became fundamental to modern number theory?
Answer: Emmy Noether
Emmy Noether's algebraic ideas became fundamental to modern number theory.
Question 9
Which prolific collaborator is identified with many problems in combinatorial and analytic number theory?
Answer: Paul Erdős
Paul Erdős collaborated on many problems in combinatorial and analytic number theory.
Question 10
Which university is named as an important institutional home for modern work in number theory?
Answer: Columbia University
Columbia University has been an important institutional home for modern work in number theory.
Question 11
Which institution in Japan is noted for significant research activity in arithmetic geometry and number theory?
Answer: Kyoto University
Kyoto University has hosted significant research activity in arithmetic geometry and number theory.
Question 12
Which city is noted for a long university tradition linked to algebraic number theory?
Answer: Heidelberg
Heidelberg has a long university tradition linked to algebraic number theory.
Question 13
The Riemann hypothesis is about the zeros of what function?
Answer: the zeta function
The Riemann hypothesis concerns the zeros of the zeta function.
Question 14
In what year was Disquisitiones Arithmeticae published?
Answer: 1801
Disquisitiones Arithmeticae was published in 1801.
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