Relatively Prime Numbers And Polynomials - Varsity Tutors

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Relatively Prime Numbers and Polynomials

Study Guide

Key Definition

Two numbers are relatively prime if their greatest common factor (GCF) is $1$.

Important Notes

  • If two numbers are relatively prime, $\gcd(a, b) = 1$
  • Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.
  • The GCF of $20$ and $33$ is $1$, so they are relatively prime.
  • Relatively prime numbers can help factor complex polynomials.
  • Understanding relatively prime numbers is useful in fractions and ratios.

Mathematical Notation

$\gcd(a, b)$ means greatest common divisor of $a$ and $b$$+$ represents additionRemember to use proper notation when solving problems

Why It Works

Relatively prime numbers have a GCF of $1$ because they share no other common factors.

Remember

Factors of a number divide evenly into it, and $\gcd(a, b) = 1$ when $a$ and $b$ are relatively prime.

Quick Reference

Relatively Prime Definition:$\gcd(a, b) = 1$

Understanding Relatively Prime Numbers and Polynomials

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

Simple explanation: Two numbers are relatively prime if their GCF is $1$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the GCF of $20$ and $33$?

A$1$B$2$C$3$D$5$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

You have 20 stickers and your friend has 33 stickers. Determine if the number of stickers you both have are relatively prime.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Consider the polynomials $p(x)=3x^2+4x+5$ and $q(x)=2x^2+9x+7$. Determine if their coefficients are relatively prime.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

If $\gcd(a, b)=1$ and $\gcd(b, c)=1$, which of the following statements is true?

A$\gcd(a, c)=1$B$\gcd(a, c)\text{ may not equal }1$C$\gcd(a,b,c)=1$D$b\mid (a+c)$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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