How to Use factorization in a Sentence

factorization

noun

• The size of a p-adic number is determined by the prevalence of p in its prime factorization.
  — Quanta Magazine, 19 Oct. 2020
• Quantum computers, though, may be able to solve integer factorization problems many millions of times faster.
  — Sara Castellanos, WSJ, 9 Oct. 2020
• Gauss also conjectured that there are only nine negative square roots that preserve prime factorization.
  — Kevin Hartnett, Quanta Magazine, 2 Mar. 2017
• The idea is to express the matrix as a product of simpler matrices—similar to the prime factorization of a number.
  — Manon Bischoff, Scientific American, 17 Aug. 2023
• This can easily be broken with Fermat's factorization method.
  — Dan Goodin, Ars Technica, 14 Mar. 2022
• So far, Böck has identified only a handful of keys in the wild that are vulnerable to the factorization attack.
  — Dan Goodin, Ars Technica, 14 Mar. 2022
• The size of the class group associated with any extension of the integers is a barometer for how much unique factorization breaks down.
  — Leila Sloman, Quanta Magazine, 12 Jan. 2023
• Unique prime factorization is a way of constructing a number system from fundamental building blocks.
  — Kevin Hartnett, Quanta Magazine, 2 Mar. 2017
• Light beams might be used to create optical computers powerful enough to solve difficult problems such as factorization.
  — Quanta Magazine, 30 Sep. 2020
• As a result, in this ring, unique prime factorization — a central tenet of arithmetic, one practically taken for granted in the normal integers — breaks down.
  — Jordana Cepelewicz, Quanta Magazine, 10 Aug. 2022
• Also called prime factorization, this math problem is unbelievably difficult for classical computers to solve.
  — Skip Sanzeri, Forbes, 25 Jan. 2023
• Quantum computing speeds up prime number factorization, thus making attacks against cryptography much more efficient.
  — Bernard Marr, Forbes, 10 Nov. 2022
• The one-way function for RSA works in a similar manner but relies on the multiplication and factorization of large prime numbers.
  — Jeanne Timmons, Ars Technica, 20 Sep. 2023
• Suddenly, mathematicians learned to apply tools like modular arithmetic and factorization to these new number systems.
  — Quanta Magazine, 1 Nov. 2023
• To optimize speed, the library uses a structure of underlying prime numbers that makes the keys much more susceptible to a mathematical process known as factorization.
  — Dan Goodin, Ars Technica, 23 Oct. 2017
• The new research shows that an algorithm using quantum Fourier transforms can perform this factorization efficiently.
  — Aman Tripathi, Interesting Engineering, 11 Sep. 2025
• However, researchers have been exploring ways to map problems like integer factorization onto the quantum annealing framework.
  — Craig S. Smith, Forbes, 16 Oct. 2024
• The authors note that a variety of other calculations, like factorization and matrix manipulations, can be performed using phase change memory arrays, meaning this isn't a one-trick pony.
  — John Timmer, Ars Technica, 26 Oct. 2017
• Everything from credit-card transactions to text messaging is encrypted using an algorithm that relies on factorization, or reverse multiplication.
  — Jack Nicas, WSJ, 16 Oct. 2017
• To boost performance, the Infineon library constructs the keys' underlying prime numbers in a way that makes the keys prone to a process known as factorization, which exposes the secret numbers underpinning their security.
  — Dan Goodin, Ars Technica, 16 Oct. 2017
• The factorization can be dramatically accelerated by spreading the load onto multiple computers.
  — Dan Goodin, Ars Technica, 16 Oct. 2017
• In 1994, physicist Peter Shor presented an algorithm that showed that a problem a classic computer would take billions of years to solve—factorization of large prime numbers—could be completed in a few days by a quantum computer.
  — Susan Lahey, Popular Mechanics, 12 May 2023
• Even more importantly, mathematicians are constantly developing new algorithms that allow for easier factorization.
  — Adam Mann, WIRED, 7 June 2013
• For this reason, the RSA cryptosystem, an encryption scheme that derives its security from the difficulty of integer factorization, remains a popular tool for secure communication.
  — Quanta Magazine, 15 May 2017