Problem 133 - Introductory and Intermediate Algebra for College Students 4th

Question

Describe the difference between a prime number and a composite number.

Step-by-Step Solution

Answer

The primary difference between prime and composite numbers is in their divisors. Prime numbers are those numbers which have exactly two distinct positive divisors (1 and the number itself), while composite numbers have more than two divisors.

Step 1: Define Prime Number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, it has only two positive divisors. Examples of prime numbers are 2, 3, 5, 7, 11, etc.

Step 2: Define Composite Number

A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, it has more than two positive divisors. Examples of composite numbers are 4, 6, 8, 9, 10, etc.

Step 3: Highlight Differences

The key difference between prime and composite numbers lies in the number of divisors. A prime number has exactly two distinct positive divisors, whereas a composite number has more than two divisors.