Prime Factorization

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What is prime factorization?

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Prime factorization is the process of expressing a number as the product of its prime factors.

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What are prime numbers?

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Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.

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How do you find the prime factorization of a number?

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To find the prime factorization of a number, divide the number by the smallest prime number until the result is 1, recording the prime factors.

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What is the prime factorization of 60?

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The prime factorization of 60 is 2² • 3 • 5.

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What is the prime factorization of 108?

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The prime factorization of 108 is 2² • 3³.

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What is the prime factorization of 81?

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The prime factorization of 81 is 3⁴.

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What is the prime factorization of 30?

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The prime factorization of 30 is 2 • 3 • 5.

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Why is it important to write prime factorization in order?

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Writing prime factorization in order (least to greatest) helps in understanding the structure of the number and is a standard convention.

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What is the Fundamental Theorem of Arithmetic?

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The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be uniquely represented as a product of prime numbers, up to the order of the factors.

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Can prime factorization be used to find the greatest common divisor (GCD)?

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Yes, prime factorization can be used to find the GCD by identifying the common prime factors and taking the lowest power of each.