Types and Properties of Numbers

Natural Numbers: Positive integers (1, 2, 3, …).
Whole Numbers: Natural numbers including zero (0, 1, 2, 3, …).
Integers: Whole numbers and their negatives (…, -3, -2, -1, 0, 1, 2, 3, …).
Rational Numbers: Numbers that can be expressed as a fraction of two integers (e.g., 1/2, 3/4).
Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., √2, π).
Real Numbers: All rational and irrational numbers.
Complex Numbers: Numbers in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

Even Numbers: Divisible by 2 (e.g., -4, 0, 2, 4).
Odd Numbers: Not divisible by 2 (e.g., -3, 1, 3, 5).
Prime Numbers: Greater than 1, only divisible by 1 and itself (e.g., 2, 3, 5, 7).
Composite Numbers: Greater than 1, divisible by numbers other than 1 and itself (e.g., 4, 6, 8).

Divisibility: A number is divisible by another if there is no remainder.
Factors: Numbers that divide another number evenly.
Multiples: The result of multiplying a number by an integer.
Greatest Common Divisor (GCD): Largest number that divides two or more numbers.
Least Common Multiple (LCM): Smallest multiple that is exactly divisible by two or more numbers.

Natural Numbers: Sequence of positive integers starting from 1 (1, 2, 3, …).
Whole Numbers: Natural numbers including zero (0, 1, 2, 3, …).
Integers: Includes all whole numbers and their negative counterparts (…, -3, -2, -1, 0, 1, 2, 3, …).
Rational Numbers: Can be expressed as a fraction where both the numerator and denominator are integers (e.g., 1/2, 3/4).
Irrational Numbers: Cannot be expressed as fractions; their decimal representations are non-repeating and non-terminating (e.g., √2, π).
Real Numbers: Encompasses all rational and irrational numbers, forming the complete number line.
Complex Numbers: Formed of a real part (a) and an imaginary part (b) combined as a + bi, where i represents the imaginary unit.

Even Numbers: Integers divisible by 2, including negatives and zero (e.g., -4, 0, 2, 4).
Odd Numbers: Integers not divisible by 2, both positive and negative (e.g., -3, 1, 3, 5).
Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves (e.g., 2, 3, 5, 7).
Composite Numbers: Natural numbers greater than 1 that have divisors other than just 1 and themselves (e.g., 4, 6, 8).

Decimal System: Base-10 numeral system that uses digits 0-9 for representation.
Binary System: Base-2 system using only two digits, 0 and 1, commonly used in computing.
Octal System: Base-8 numeral system employing digits 0-7.
Hexadecimal System: Base-16 system that includes digits 0-9 and letters A-F to represent values.

Addition: Process of finding the total or sum by combining numbers.
Subtraction: Determining the difference between two numbers.
Multiplication: Involves repeated addition of a number for a specified number of times.
Division: Operation that splits a number into a specified number of equal parts.

Follow the sequence: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Divisibility: A condition where one number can be divided by another without leaving a remainder.
Factors: Whole numbers that divide another number exactly without leaving a remainder.
Multiples: Results obtained by multiplying a given number by any integer.
Greatest Common Divisor (GCD): The largest integer that can divide two or more numbers without a remainder.
Least Common Multiple (LCM): The smallest integer that is a multiple of two or more numbers.

Mathematics: Foundation for various branches of math, including algebra, geometry, and statistics.
Science: Involves numerical measurements for calculations, experiments, and data analysis.
Finance: Critical in managing budgets, conducting accounting, and performing economic assessments.
Technology: Integral to programming languages, algorithms, and data manipulation in computing.