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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 deals with the properties and relationships of numbers, such as factors, prime numbers, and divisibility.
Factors
A factor of a number is any number that can be multiplied to produce the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Practice Questions
- What are the factors of 15?
- What are the factors of 24?
- What are the factors of 28?
Prime Numbers
A prime number is a number that is only divisible by itself and 1. For example, the first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Practice Questions
- What are the first ten prime numbers?
- What is the next prime number after 19?
- What is the prime number before 11?
Divisibility
Divisibility is a way of determining whether a number can be divided evenly by another number. For example, a number is divisible by 4 if the number can be divided evenly by 4 (no remainder).
Practice Questions
- Is 8 divisible by 4?
- Is 16 divisible by 3?
- Is 25 divisible by 5?
Prime Factorization
Prime factorization is the process of breaking a number down into its prime factors. For example, the prime factorization of 12 is 2 x 2 x 3.
Practice Questions
- What is the prime factorization of 20?
- What is the prime factorization of 30?
- What is the prime factorization of 45?
