# Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q5

My Solution for "Show that any composite three-digit number must have a prime factor less than or equal to $31$."

## Table of Contents

This is my solution for Chapter 3.2 Q5 in the book *Elementary Number Theory 7th Edition* written by David M. Burton.

## Background

All theorems, corollaries, and definitions listed in the book's order:

**I will only use theorems or facts that are proved before this question**. So you will not see that I quote theorems or facts from the later chapters.

## Question

Show that any composite three-digit number must have a prime factor less than or equal to $31$.

## Solution

Using the Property of Composite Numbers, the largest three-digit number $999$ will possess a prime divisor $p$ where $p \leq \sqrt{999} \approx 31.6$. Therefore, any composite three-digit number must have a prime factor less than or equal to $31$.

**Read More:** All My Solutions for This Book

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