Prime Numbers - Prime Factorization

Prime number is a whole number greater than 1, whose only two whole-number factors are 1 and itself.

ℙ = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29 \dots}

1 and 0 are not prime numbers because 1 has one divisor and 0 has an infinite number of divisors.

Prime Factorization

Any positive integer m can be written as a unique product of prime numbers:

\begin{matrix} m = {p_{1}}^{α_{1}} \cdot {p_{2}}^{α_{2}} \cdot . . . \cdot {p_{k}}^{α_{k}} \\ p_{1,} p_{2,} . . ., p_{k} \in ℙ \\ α_{1}, α_{k}, . . ., α_{k} \in ℕ \end{matrix}

Example:

\begin{matrix} 60 & | & 2 \\ 30 & | & 5 \\ 6 & | & 2 \\ 3 & | & 3 \\ 1 & | \end{matrix}

60 = 2^{2} \cdot 3 \cdot 5

Keywords:

General Information
Symbols, and relationships in mathematics
Number theory
Number Sets
Prime Numbers - Prime Factorization
Divisibility Rules
Greatest Common Divisor (factor) - Least Common Multiple
Operations with rational numbers
Binomial theorem
Binomial theorem
Combinatorics
Permutations
Combination
Variation
Sets
Operations on Sets
Cardinality of sets
Fundamental laws of set algebra
Cartesian product
Relation
Logic
Logical Operations and Truth Tables
Properties of Logical Operators
Graph Theory
Graph Theory - definitions, relationships