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Chapter 1: Problem 13

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$22$$

Short Answer

Expert verified
The number 22 is a composite number, and its prime factorization is \(2 \times 11\).

Step by step solution

01

Identify if the number is prime or composite

First, check if the number 22 has any divisors other than 1 and itself. Since 22 can be divided evenly by 2 and 11, it is not a prime number, so it must be a composite number.
02

Find the prime factorization of the composite number

Next, find the prime numbers that multiply together to give 22. This can be done by dividing 22 by prime numbers, starting from the smallest (2, 3, 5, 7, 11, 13, ...), and continuing till there are only prime numbers left. 22 divided by 2 gives 11, and since 11 is a prime number, the prime factorization ends here.

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