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Irrational numbers cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions. Example: The number $\pi$ is irrational.

Imaginary numbers are a subset of complex numbers that can be written as a real number multiplied by the imaginary unit $i$. Example: $2i$ is an imaginary number, where $i = \sqrt{-1}$.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Example: 7 is a prime number because its only divisors are 1 and 7.

A perfect square is an integer that is the square of an integer. Example: 49 is a perfect square because $7 \times 7 = 49$.

Integers are all the whole numbers including negative numbers, zero, and positive numbers. Example: -3, 0, and 4 are all integers.

The least common multiple (LCM) of two integers is the smallest number that is a multiple of both of the integers. Example: The LCM of 4 and 5 is 20.

Rational numbers are numbers that can be expressed as a fraction of two integers where the denominator is not zero. Example: $\frac{1}{2}$ and $\frac{4}{3}$ are rational numbers.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. Example: The sequence 2, 4, 6, 8 is arithmetic with a common difference of 2.

A geometric sequence is a sequence of numbers where each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. Example: The sequence 3, 9, 27, 81 is geometric with a common ratio of 3.

Real numbers include all the rational and irrational numbers. They correspond to points on the number line. Example: $\frac{3}{4}$, $\pi$, and -2 are all real numbers.

A number is divisible by another if it can be divided by the other number without leaving a remainder. Example: 10 is divisible by 2 because $10 \div 2 = 5$ with no remainder.

The absolute value of a real number is the non-negative value of that number without regard to its sign. Example: The absolute value of -7 is 7.

A multiple of a number is the product of that number and any integer. Example: 20 is a multiple of 5 because $5 \times 4 = 20$.

Natural numbers are the set of positive integers beginning from 1. Example: The first five natural numbers are 1, 2, 3, 4, and 5.

The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. Example: The GCD of 8 and 12 is 4.

A factor of a number is an integer which divides the number without leaving a remainder. Example: 3 is a factor of 12 because $12 \div 3 = 4$ with no remainder.

The Euclidean Algorithm is a method for finding the greatest common divisor (GCD) of two numbers. It is based on the principle that the GCD of two numbers also divides their difference. Example: GCD of 270 and 192 can be found using the Euclidean Algorithm.