Fundamentals of Number Theory

Mathematics

A collection of standard number theory problems covering divisibility, prime numbers, modular arithmetic, and sequences.

number theory prime numbers divisibility modular arithmetic

18 Questions Medium Ages 14+ Oct 23, 2026

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About this Study Set

This study set covers Mathematics through 18 practice questions. A collection of standard number theory problems covering divisibility, prime numbers, modular arithmetic, and sequences. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

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Browse all 18 questions from the Fundamentals of Number Theory study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 Which of the following is the definition of a perfect number?

A A number equal to the sum of its proper divisors
B A number that is the square of a prime
C A number with exactly two factors
D A number that is prime in base 10

2 What is the greatest common divisor (GCD) of 48 and 72?

A 8
B 12
C 24
D 36

3 According to the Fundamental Theorem of Arithmetic, every integer greater than 1 can be represented as:

A A unique sum of two primes
B A unique product of prime numbers
C A unique power of 2
D A unique sequence of squares

4 What is the result of 17 modulo 5?

5 Which of the following numbers is a Mersenne prime?

A 9
B 15
C 31
D 33

6 What is the smallest prime number?

7 How many factors does the number 12 have?

8 Which theorem states that if p is prime, then a^p ≡ a (mod p) for any integer a?

A Wilson's Theorem
B Fermat's Little Theorem
C Euler's Totient Theorem
D Chinese Remainder Theorem

9 What is the sum of the first 5 positive integers?

A 10
B 15
C 20
D 25

10 Which of these numbers is coprime to 14?

A 2
B 7
C 9
D 21

11 The value of Euler's totient function φ(10) is:

12 What is the least common multiple (LCM) of 6 and 8?

A 12
B 16
C 24
D 48

13 A number is divisible by 3 if and only if:

A The last digit is even
B The last two digits are divisible by 3
C The sum of its digits is divisible by 3
D The number ends in 3, 6, or 9

14 Which of the following is a composite number?

A 13
B 17
C 21
D 23

15 What is the prime factorization of 60?

A 2^2 × 3 × 5
B 2 × 3^2 × 5
C 2 × 3 × 5^2
D 2^3 × 3 × 5

16 In modular arithmetic, what is the inverse of 3 modulo 7?

17 What is the 6th term of the Fibonacci sequence, starting with 1, 1, 2, 3, 5...?

A 6
B 8
C 10
D 13

18 Which property describes that for any integers a and b, a + b = b + a?

A Associative
B Distributive
C Commutative
D Identity

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