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Number Theory in Global Context

Number Theory

A collection of challenging number theory problems connected to geographical and global data.

mathematics geography statistics

12 Questions Hard Ages 15+ Sep 22, 2026

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About this Study Set

This study set covers Number Theory through 12 practice questions. A collection of challenging number theory problems connected to geographical and global data. 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 12 questions from the Number Theory in Global Context study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 The number of independent countries in the United Nations is a prime number. What is the sum of the digits of the next prime number greater than 193?

A 13
B 14
C 15
D 16

2 The total number of time zones (including fractional offsets) is 38. What is the smallest prime factor of the number of years in a century multiplied by this number?

3 The length of the Equator is approximately 40,075 kilometers. What is the largest prime factor of the integer part of this value divided by 5?

A 167
B 173
C 179
D 181

4 The number of official languages of the United Nations is 6. How many distinct ways can you choose a committee of 3 languages from these 6, which is equivalent to the number of combinations 6C3?

A 15
B 20
C 25
D 30

5 The number of sovereign states in the world as recognized by the UN is 193. Which of the following is the primitive root modulo 193?

6 The number of states in the United States of America is 50. How many divisors does 50 have?

7 The highest peak in the world, Mount Everest, is 8,848 meters high. What is the sum of the prime factors of 8848?

A 13
B 17
C 21
D 23

8 There are 7 continents on Earth. How many positive integers less than 7 are coprime to 7?

9 The number of years in a decade is 10. What is the value of the totient function φ(10)?

10 The number of countries in the G20 is 19 (plus the EU). What is the smallest prime number greater than 19?

A 21
B 23
C 25
D 29

11 The number of letters in the official long-form name of the United Kingdom (United Kingdom of Great Britain and Northern Ireland) is 47. Is 47 a Mersenne prime?

A Yes, 2^5-1
B Yes, 2^6-1
C No, it is a Sophie Germain prime
D No, it is a composite number

12 The total number of countries in Africa is 54. What is the prime factorization of 54?

A 2*3^2
B 2*3^3
C 3*2^3
D 2^2*3^2

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