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Find the prime factorization of the number. $$36$$

   Find the prime factorization of the number.
$$36$$

Prealgebra and Introductory Algebra

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 1, Problem 159

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Solved by Expert Ashley Hanson

06/21/2020

Step 1

The smallest prime number is 2, and 36 is an even number, so it can be divided by 2. We get 36 divided by 2 equals 18. Show more…

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Find the prime factorization of the number. $$36$$

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Key Concepts

Prime Factorization

Prime factorization is the process of expressing a composite number as a product of prime numbers. This process involves breaking down the number step by step until all factors are prime, which provides a unique representation of the number according to the Fundamental Theorem of Arithmetic.

Prime Numbers

Prime numbers are integers greater than 1 that have no divisors other than 1 and themselves. They serve as the basic building blocks in number theory, and every composite number is a product of these primes.

Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that every integer greater than 1 has a unique prime factorization up to the order of the factors. This theorem provides the foundation for many concepts in number theory, including divisibility and the properties of integers.

Exponential Notation in Factorization

Exponential notation in prime factorization is a shorthand for expressing repeated multiplication of the same prime factor. For instance, if a prime number occurs multiple times in the factorization, it is written with an exponent to indicate how many times it appears.

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