Problem 27 - Introductory Algebra for College Students

Question

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$240$$

Step-by-Step Solution

Answer

The number 240 is a composite number and its prime factorization is \(2^4 \times 3 \times 5\)

Step 1: Identifying the number type

Identify if the number 240 is prime or composite. Since 240 can be divided evenly by numbers other than 1 and itself (for example 2, 3, 4, 5, 6, 8, and many others), it is a composite number.

Step 2: Finding the prime factors

The prime factorization of a number is done by dividing it by prime numbers, starting from the smallest one, which is 2. If the number is not divisible evenly, proceed to the next prime number. Keep doing this until the quotient is a prime number. For 240, we start by dividing it by 2, the smallest prime number, and we obtain 120. We then divide again by 2 and obtain 60. Continuing in this manner, the prime factorization of 240 will be \(2 \times 2 \times 2 \times 2 \times 3 \times 5\), or expressed as powers of primes, \(2^4 \times 3 \times 5\)