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Elementary Number Theory Challenge

Mathematics

A collection of advanced number theory questions covering prime properties, divisibility, and number classifications.

number theory prime numbers divisibility

8 Questions Hard Ages 5+ Oct 29, 2026

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About this Study Set

This study set covers Mathematics through 8 practice questions. A collection of advanced number theory questions covering prime properties, divisibility, and number classifications. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

Questions & Answers

Browse all 8 questions from the Elementary Number Theory Challenge 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 excluding itself
B A number that is the product of two distinct prime numbers
C A number whose digits add up to a multiple of 3
D A number that has exactly two factors

2 What is the smallest prime number that is also the sum of two consecutive prime numbers?

3 Which of these numbers is a 'composite number' that is not a 'square number'?

A 9
B 16
C 10
D 25

4 How many prime numbers exist between 1 and 20?

A 7
B 8
C 9
D 10

5 A 'Mersenne prime' is a prime number that can be expressed in which form (where n is an integer)?

A n^2 + 1
B 2^n - 1
C n^3 + 3
D 2n + 1

6 Which of the following statements about the number 1 is mathematically correct?

A It is a prime number
B It is a composite number
C It is neither prime nor composite
D It is an even number

7 What is the Greatest Common Divisor (GCD) of 24 and 36?

A 6
B 8
C 12
D 18

8 Which sequence represents the first four 'triangular numbers'?

A 1, 3, 6, 10
B 2, 4, 8, 16
C 1, 4, 9, 16
D 0, 1, 2, 3

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