Problem 24 - Introductory Algebra for College Students

Question

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$83$$

Step-by-Step Solution

Answer

The number 83 is a prime number.

Step 1: Identify the number

We are given a single number 83. We need to determine whether it is a prime number or a composite number.

Step 2: Establish a prime number check

An established way to check if a number is prime or not is to run a loop and try dividing the number from 2 to the square root of that number. If the number is divisible, then it will not be a prime number otherwise if the loop has finished and the number was not divisible by any other number apart from 1 and the number itself, then it's a prime number.

Step 3: Implementation of prime number check

Implementing the prime number check for 83, there is no number between 2 and the square root of 83 that can divide 83 evenly. Thus, 83 is a prime number.