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Greatest Common Factors

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Greatest Common Factors

Study Guide

Key Definition

The greatest common factor (GCF) is the largest whole number that divides two or more given numbers evenly. To find the GCF, use prime factorization.

Important Notes

A factor is a number that divides another number without leaving a remainder.
The GCF is always less than or equal to the smallest of the given numbers.
Prime factorization involves breaking down a number into its prime factors.
If a number is divided by its GCF, it will result in an integer.
GCF helps simplify fractions by dividing both the numerator and the denominator by their GCF.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$gcd(a, b)$ or $GCF(a, b)$ represents the greatest common factor of a and b

Remember to use proper notation when solving problems

Why It Works

The GCF is useful for simplifying fractions and finding common denominators. By using prime factorization, we ensure the accuracy of finding the GCF.

Remember

Always list all factors of a number to ensure you find the GCF accurately. Use prime factorization for complex numbers.

Quick Reference

GCF of 36 and 24:$12$

Understanding Greatest Common Factors

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Video explanation of this concept

Beginner

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Beginner Explanation

The greatest common factor (GCF) is the largest number that divides two numbers without remainder. For example, to find the GCF of 8 and 12, list factors of 8 (1, 2, 4, 8) and 12 (1, 2, 3, 4, 6, 12). The common factors are 1, 2, and 4, so the GCF is 4.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the GCF of $18$ and $24$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $36$ candies and $24$ cookies. How can you pack them equally in bags?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the GCF of $48$ and $180$ using prime factorization.

Challenge Quiz

Single Choice Quiz

Advanced

What is the GCF of $54$ and $72$?

Recap

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Review key concepts and takeaways