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Chapter 1: Problem 14

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$15$$

Short Answer

Expert verified
The number 15 is a composite number and its prime factorization is \(3 \times 5\).

Step by step solution

01

Identify the Number as Prime or Composite

Given number is 15. To determine if it's composite or prime, check if it has factors besides 1 and itself. The factors of 15 are 1, 3, 5 and 15, meaning 15 is a composite number as it has more than two factors.
02

Find the Prime Factorization of the Composite Number

The prime factorization of a composite number involves breaking down the number into its smallest prime factors. One method to find prime factors is the 'Factor Tree' method. \n\n- Begin by dividing the number 15 by the smallest prime number, which is 2. 15 is not divisible by 2, so move to the next prime number, 3. \n- 15 divided by 3 equals 5. So, the prime factors of 15 are 3 and 5. \n\nHence, the prime factorization of 15 is \(3 \times 5\).

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