Problem 15 - Introductory Algebra for College Students

Question

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$20$$

Step-by-Step Solution

Answer

20 is a composite number and its prime factorization is \(2^2 \times 5^1\).

Step 1: Identifying the number

The number given in the exercise is 20.

Step 2: Determining if the number is prime or composite

20 can be divided evenly by 1, 2, 4, 5, 10 and 20, with no remainder. Since it has more divisors than just 1 and itself, 20 is a composite number.

Step 3: Finding the prime factorization

The prime factorization of a number is the determination of the set of prime numbers which multiply together to give the original number. The prime factorization of 20 is found by dividing the number by prime numbers, starting from the lowest (i.e., 2). 20 ÷ 2 = 10. 10 is not a prime number, so divide 10 by 2 again, which equals 5. 5 is a prime number. Therefore, the prime factorization of 20 is \(2 \times 2 \times 5\) or \(2^2 \times 5^1\).