Number Theory Quiz

Multiple Choice Questions

1. What is the definition of Number Theory?

   • A) The study of positive integers
   • B) The study of negative integers
   • C) The study of real numbers
   • D) The study of complex numbers

2. What is the fundamental theorem of arithmetic?

   • A) Any positive integer can be written as a product of prime numbers
   • B) Any positive integer can be written as a sum of prime numbers
   • C) Any positive integer can be written as a difference of prime numbers
   • D) Any positive integer can be written as a quotient of prime numbers

3. What is the definition of a prime number?

   • A) A number divisible by only itself and 1
   • B) A number divisible by only itself and 2
   • C) A number divisible by only itself and 3
   • D) A number divisible by only itself and 4

True or False Questions

1. The sum of two prime numbers is always a prime number?

   • A) True
   • B) False

2. Every number can be written as a product of prime numbers?

   • A) True
   • B) False

3. The sum of two prime numbers is always an even number?

   • A) True
   • B) False

Fill in the Blank Questions

1. The __________ of a number is the number of times it can be divided by 2.

2. A _________ number is a number that has only two factors, itself and 1.

3. The sum of two prime numbers is always an ________ number.

Short Answer Questions

1. What is the definition of a composite number?

2. What is the definition of a perfect number?

3. How can you tell if a number is prime or composite?

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Number Theory Practice Sheet

Introduction

Number theory is the study of the properties of numbers and the relationships between them. It is a branch of mathematics that has been studied for centuries.

In this practice sheet, we will explore some of the basic concepts of number theory and then apply them to some practice problems.

What is a Prime Number?

A prime number is a number that is only divisible by itself and 1. For example, 2, 3, 5, 7 and 11 are all prime numbers.

What is a Composite Number?

A composite number is a number that is not prime. It is a number that can be divided by more than just itself and 1. For example, 4, 6, 8, 9 and 10 are all composite numbers.

What is a Factor?

A factor is a number that can divide another number evenly. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.

What is a Common Factor?

A common factor is a factor that two or more numbers have in common. For example, the common factors of 12 and 18 are 1, 2, 3 and 6.

What is a Greatest Common Factor (GCF)?

The greatest common factor (GCF) is the largest common factor of two or more numbers. For example, the GCF of 12 and 18 is 6.

What is a Least Common Multiple (LCM)?

The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 12 and 18 is 36.

Practice Problems

1. What is the GCF of 24 and 36?

Answer: The GCF of 24 and 36 is 12.

1. What is the LCM of 15 and 20?

Answer: The LCM of 15 and 20 is 60.

1. What is the sum of the prime numbers between 20 and 30?

Answer: The sum of the prime numbers between 20 and 30 is 97 (23 + 29).

1. What is the sum of the common factors of 24 and 36?

Answer: The sum of the common factors of 24 and 36 is 42 (1 + 2 + 3 + 6 + 12 + 18).

1. What is the product of the prime numbers between 10 and 20?

Answer: The product of the prime numbers between 10 and 20 is 9699690 (11 x 13 x 17 x 19).