Greatest Common Factor
Find the greatest common factor (GCF) of two or more numbers in Grade 6 math using lists of factors or prime factorization — apply GCF to simplify fractions efficiently.
Key Concepts
Property The greatest common factor is the greatest number that is a factor of each of two or more numbers.
Examples To reduce $\frac{60}{100}$, the GCF of 60 and 100 is 20, so the fraction becomes $\frac{3}{5}$. To reduce $\frac{24}{100}$, the GCF of 24 and 100 is 4, so the fraction becomes $\frac{6}{25}$. To reduce $\frac{75}{100}$, the GCF of 75 and 100 is 25, so the fraction becomes $\frac{3}{4}$.
Explanation Think of the GCF as your fraction simplifying superpower! It's the biggest number that can divide evenly into both the top and bottom numbers of a fraction. Using the GCF lets you reduce a fraction in one giant leap instead of taking lots of little baby steps. It’s the most efficient way to get your fraction to its simplest form!
Common Questions
What is the greatest common factor (GCF)?
The GCF of two numbers is the largest number that divides evenly into both of them. For example, the GCF of 12 and 18 is 6, because 6 divides both 12 and 18 with no remainder.
How do you find the GCF using lists of factors?
List all factors of each number, then identify the common factors. The largest number on both lists is the GCF. For 12: 1,2,3,4,6,12 and 18: 1,2,3,6,9,18 — common factors are 1,2,3,6, so GCF = 6.
How is the GCF used to simplify fractions?
To simplify 12/18, find the GCF of 12 and 18, which is 6. Divide both numerator and denominator by 6 to get 2/3. Dividing by the GCF in one step gives the fraction in lowest terms directly.
What is the difference between GCF and LCM?
GCF (Greatest Common Factor) is the largest shared factor — used to simplify fractions. LCM (Least Common Multiple) is the smallest shared multiple — used to find common denominators for adding fractions.