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 $31$."

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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:

Theorems and Corollaries in Elementary Number Theory (Ch 1 - 3)
All theorems and corollaries mentioned in David M. Burton’s Elementary Number Theory are listed by following the book’s order. (7th Edition) (Currently Ch 1 - 3)
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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

< Chapter 3.2, Q4 Chapter 3.2, Q6 >

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