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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.

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.

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.

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

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

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.

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

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.

Complex numbers consist of all numbers that can be expressed in the form $a + bi$ where $a$ and $b$ are real numbers and $i$ is the imaginary unit. Example: 3 + 4i is a complex number.

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 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.

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.

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

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.

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.

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

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.