Problem 14 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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 \(3 \times 5\).