## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 5 - Number Theory and the Real Number System - 5.1 Number Theory: Prime and Composite Numbers - Exercise Set 5.1 - Page 258: 127

#### Answer

Eratosthenes sieve method: Eratosthenes sieve method is used to determine the prime numbers up to any given limits. By using this method all those numbers are rejected which have the others factor except number and$1$. The process of finding the prime numbers is shown below example. Example: Consider some numbers as, from $2$to$50$. Steps to determine the prime numbers by using Eratosthenes sieve method. Step 1: Reject all numbers of multiple$\left( 2 \right)$ Step 2: Reject all numbers of multiple$\left( 3 \right)$. Step 3: Reject all number of multiple$\left( 5 \right)$. Step 4: Reject all numbers of multiple$\left( 7 \right)$. Step 5: Reject all numbers of multiple$\left( 11 \right)$. Now, the remaining numbers are prime numbers that are not multiples of other numbers except$1$. So, the prime numbers from $\left( 2 \right)$to $\left( 50 \right)$are, $2,3,5,7,11,13,17,19,23,27,31,37,41,43,47$ Hence, from above observation, the prime numbers are determined from by rejecting that numbers which are multiples of other numbers

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