factorize

Meanings

• Verb

  To break down a number into its factors or prime factors.

  - "Can you factorize the number 24?"
  - "The prime factors of 25 are 5 and 5."

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Variants

List of all variants of factorize that leads to same result
factorization , factorizations , factorize , factorized , factorizes , factorizing

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Etymology

origin and the way in which meanings have changed throughout history.

The word 'factorize' comes from the Latin word 'factor' meaning 'doer or maker', and the suffix '-ize' which means 'to make or do'. In mathematics, it refers to the process of finding the factors or prime factors of a given number.

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Trivia

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1. The largest known prime number is 2^82,589,933-1, which has over 24 million digits.

2. The smallest composite number is 4, which is the sum of 1 and 3.

3. The number 1 is neither prime nor composite, as it has only one positive divisor: 1 itself.

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Related Concepts

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1. Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, and 7 are prime numbers.

2. Composite number: A composite number is a natural number greater than 1 that has at least one positive divisor other than 1 and itself. For example, 4, 6, and 8 are composite numbers.

3. Factor theorem: The factor theorem states that if p is a prime number and a is an integer, then p is a factor of a if and only if a is a factor of p.

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Culture

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Factorization is a fundamental concept in number theory and has applications in various fields such as cryptography, physics, and engineering.

How to Memorize "factorize"

1. visualize
   

   - To memorize the concept of factorization, you can visualize breaking down a number into smaller parts. For example, you can imagine 24 as 2 times 2 times 2 times 2.
   - Another way to visualize factorization is by drawing a tree diagram, where each factor is represented by a branch.

2. associate
   

   - You can associate the word 'factorization' with the word 'factors'. Try to remember that 'factorization' is the process of finding the factors of a number.
   - Another association you can make is with the multiplication table. Factorization is essentially the reverse process of finding the prime factors of numbers in the multiplication table.

3. mnemonics
   

   - One mnemonic to remember the process of factorization is 'Divide and Conquer'. Try to divide the number into smaller parts and conquer each part by finding its factors.
   - Another mnemonic is 'Four Fs of Factoring': Factors, Find, Factorize, and Factor Tree.

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