Learn number concepts

A prime number is a whole number greater than 1 that has exactly two positive divisors: 1 and itself. Primes are the building blocks of all integers through multiplication.

A composite number is a whole number greater than 1 that has more than two positive divisors. Composite numbers can always be written as a product of two smaller whole numbers greater than 1.

A factor (or divisor) of a number is a whole number that divides it evenly with no remainder. Factoring helps simplify fractions, find GCD, and break numbers into products.

A divisor of an integer is a number that divides it evenly. The terms divisor and factor mean the same thing in whole-number arithmetic.

Prime factorization writes a whole number greater than 1 as a product of prime numbers. Every integer has exactly one such factorization, apart from the order of factors.

Even numbers are divisible by 2; odd numbers are not. Every integer is either even or odd, and this parity property affects arithmetic, algebra, and patterns in sequences.

A perfect number equals the sum of its proper divisors (all positive divisors except itself). The smallest perfect numbers are 6 and 28.

An abundant number is a positive integer whose proper divisors add up to more than the number itself. Twelve is the smallest abundant number.

A deficient number is a positive integer whose proper divisors sum to less than the number itself. Most small integers, including all primes, are deficient.

The Fibonacci sequence starts with 0 and 1, and each subsequent term is the sum of the two before it. These numbers appear in nature, art, and many mathematical patterns.

A triangular number counts dots arranged in an equilateral triangle. The nth triangular number equals the sum of the first n positive integers.

A square number (or perfect square) is the product of an integer with itself. Square numbers form the sequence 0, 1, 4, 9, 16, 25, and so on.

A cube number (or perfect cube) is an integer that equals some integer raised to the third power. Cube numbers represent the volume of a cube with integer edge length.

A palindrome number reads the same forward and backward. Examples include 121, 1331, and 9009. Palindromes are defined by digit symmetry, not by mathematical operations.

The binary system uses base 2, with digits 0 and 1 only. Computers store and process all data in binary because electronic circuits naturally represent two states: on and off.

Hexadecimal (base 16) uses digits 0–9 and letters A–F. It compactly represents binary values and is widely used in programming, memory addresses, and color codes.

Roman numerals represent numbers using letters from the Latin alphabet: I, V, X, L, C, D, and M. They use additive and subtractive rules and appear on clocks, outlines, and historical inscriptions.

The digit sum of a number is the total obtained by adding its individual digits. Digit sums help with divisibility checks, checksums, and recreational number tricks.

The greatest common divisor of two or more integers is the largest positive integer that divides all of them evenly. GCD is essential for simplifying fractions and solving Diophantine equations.

The least common multiple of two or more integers is the smallest positive integer divisible by all of them. LCM is used to add fractions and find repeating cycle lengths.