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Guilherme Mazui

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What is the Difference Between Prime Number and Prime Factors?

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The difference between prime numbers and prime factors lies in their definition and relationship with other numbers:

  • Prime Number: A prime number is a natural number greater than one that is divisible only by one and the number itself. Prime numbers have only two factors, one and the number itself. The first few prime numbers are 2, 3, 5, 7, 11, and so on.
  • Prime Factor: A prime factor is a factor of a number that is also a prime number. In other words, a prime factor is one of the smallest components of a number, and it can only be divided by 1 and by itself. Prime factors are the factors of a number that are also prime numbers.

For example, consider the number 32. The factors of 32 are 1, 2, 4, 8, and 16. However, the prime factors of 32 are only 2 and 16, as they are prime numbers. The other factors, 1, 4, and 8, are not prime factors because they are composite numbers with more than two factors.

In summary:

  • A prime number has only two factors, one and the number itself.
  • A prime factor of a number is a factor and also a prime number.
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  • What is the Difference Between Prime Number and Prime Factors?
  • Comparative Table: Prime Number vs Prime Factors

    • Comparative Table: Prime Number vs Prime Factors

    Here is a table that highlights the differences between prime numbers and prime factors:

    Feature Prime Numbers Prime Factors
    Definition A prime number is a natural number greater than 1 that has exactly two factors: 1 and the number itself. A prime factor is a prime number that can be used to divide another number completely and cannot be split into more prime factors.
    Examples Prime numbers include 2, 3, 5, 7, 11, and so on. Prime factors of a number are the prime numbers that are multiplied to get the original number. For example, 2 and 5 are the prime factors of 20, i.e., 2 × 2 × 5 = 20.
    Relationship A prime number can only have 1 and the number itself as its factors. Prime factors are used to express a number as a product of primes through prime factorization.

    In summary, prime numbers are a subset of natural numbers with exactly two factors, while prime factors are prime numbers used to divide another number completely during prime factorization.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.