A list of factors.
Used in a Sentence
factorization
Definitions, parts of speech, synonyms, and sentence examples for factorization.
Editorial note
Factorization is NP, so having a fast way of solving NP-complete problem would yield a way to solve factorization as well.
Examples16
Definitions3
Parts of speech1
Quick take
A list of factors.
Meaning at a glance
The clearest senses and uses of factorization gathered in one view.
(mathematics) The process of creating a list of factors.
(mathematics) An expression listing items that, when multiplied together, will produce a desired quantity.
Definitions
Core meanings and parts of speech for factorization.
noun
A list of factors.
See also: factoring, factorisation
noun
(mathematics) The process of creating a list of factors.
See also: factoring, factorisation
noun
(mathematics) An expression listing items that, when multiplied together, will produce a desired quantity.
See also: factoring, factorisation
Example sentences
Factorization is NP, so having a fast way of solving NP-complete problem would yield a way to solve factorization as well.
It is the largest of the RSA numbers and carried the largest cash prize for its factorization, US$200,000.
Look up some of the prime factorization prizes and do the math to see if it is achievable.
We use those technologies to drive production algorithms that incorporate bayesian inference, multi-armed bandits, matrix factorization, and collaborative filtering.
You can easily extend prime factorization to rational numbers by allowing negative as well as nonnegative exponents for primes.
And depending on what your notion of a whole complex number is, they have unique prime factorization as well.
It's just in the context of the whole numbers (i.e., integers) that 6 has specifically the prime factorization 2 x 3.
Well, at the very least, trusting them to do that responsibly as long as there is no algorithm for faster large prime factorization, and the message is unreadable to them anyway.
Therefore, for every prime, x's prime factorization contains an even number of it as well.
It turns out that Z[r_p] has unique factorization if p is a regular prime[3].
The prime factorization for 6 (and any other rational) will still be unique.
This is in opposition to what happens in the integers, namely unique factorization of any integer (other than 0, 1, or -1) into primes.
Quote examples
In essence, RSA is a crypto-algorithm that relies on the fact that "Factorization" is a very very hard mathematical problem for standard computers to solve.
"Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer." 1994.
In the mentioned context of the reals, or even just the rationals, we could instead note that 6 (or anything, really) could continue being divided indefinitely, thus having no particular "prime factorization" in the sense of a factorization which cannot be further refined.
The inability to further factor 2, 3, 5, 7, 11, etc., which causes us to single them out as "prime" in the first place, is only on an account of factorization into whole numbers excluding such rational factorizations.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use factorization in a sentence?
Factorization is NP, so having a fast way of solving NP-complete problem would yield a way to solve factorization as well.
What does factorization mean?
A list of factors.
What part of speech is factorization?
factorization is commonly used as noun.