**Music**

Determining **factors** of numbers or frequencies determines their degree of harmonicity, affinity or attraction. [Dale Pond]

In Mathematics, **factorization** (also **factorisation** in British English) or **factoring** is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or **factors**, which when multiplied together give the original. For example, the number 15 **factors** into primes as 3, 5, and the polynomial x^{2}ˆ4 **factors** as (xˆ2)(x + 2). In all cases, a product of simpler objects is obtained.

The aim of **factoring** is usually to reduce something to "basic building blocks" (least common denominator), such as numbers to prime numbers, or polynomials to irreducible polynomials. **Factoring** integers is covered by the fundamental theorem of arithmetic and **factoring** polynomials by the fundamental theorem of algebra. Vieta's formulas relate the coefficients of a polynomial to its roots.

The opposite of polynomial **factorization** is expansion, the multiplying together of polynomial **factors** to an "expanded" polynomial, written as just a sum of terms.

Integer **factorization** for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.

A matrix can also be **factorized** into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.

Another example is the **factorization** of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a subjective function with an injective function. This situation is generalized by **factorization** systems. Wikipedia, Factoring

You can **factor** numbers/frequencies here:
Wolfram Mathematica, Factoring

See Also

**Affinity**
**Aliquot**
**Fast Fourier Transform**
**Figure 8.14 - Some Basic Waveforms and their constituent Aliquot Parts**
**Finite Element Analysis**
**Fundamental**
**Graduation**
**Harmonic**
**Harmonicity**
**Harmony**
**Interval**
**Law of Cycles**
**Modal Analysis**
**Music**
**Note**
**Octave prime**
**Overtone Series**
**Overtone**
**Partial**
**prima materia**
**PRIMARY IMPULSES**
**prime mover**
**Prime Neutral Center**
**Prime Numbers**
**Prime Third**
**prime thirds**
**prime**
**Ramsay - Rationale of the Limit of Musical Mathematical Primes**
**Ramsay - Tendencies of the Notes form Proximity and Affinity**
**three primary centers**
**three primary ratios**
**two prime conductors**