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Greatest Common Factor of Monomials

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Greatest Common Factor of Monomials

Study Guide

Key Definition

The greatest common factor (GCF) of monomials is the product of all common factors. For example, in $-27p^2qr^5$ and $15p^3r^3$, the GCF is $3p^2r^3$.

Important Notes

The GCF is found by multiplying all the common factors.
Prime factorization helps identify common factors.
$-1$ is included if necessary.
Variables are treated as factors in prime factorization.
The GCF must include the lowest exponent of each common variable.

Mathematical Notation

$\times$ represents multiplication

$p^2$ indicates the power of a variable

$\frac{a}{b}$ represents a fraction

$\sqrt{x}$ represents the square root

Remember to use proper notation when solving problems

Why It Works

The GCF ensures that you are working with the simplest form, which simplifies equations and calculations.

Remember

Always factor completely and check each factor's exponent.

Quick Reference

Common Factor Example:$3p^2r^3$ from $-27p^2qr^5$ and $15p^3r^3$

Understanding Greatest Common Factor of Monomials

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Video explanation of this concept

Beginner

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Beginner Explanation

The GCF is the largest factor shared by both monomials. First, write each monomial's prime factorization, then multiply the common prime factors together.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the GCF of $12x^2y$ and $18xy^2$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have two different sets of items. One set contains $24a^3b^2$ and the other $36a^2b^3$. Determine the largest possible identical group size.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine the GCF of $-45x^3y$ and $75xy^2$.

Challenge Quiz

Single Choice Quiz

Advanced

What is the GCF of $-54x^4y^3$ and $90x^2y^5$?

Recap

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Review key concepts and takeaways