>[!summary] The greatest common divisor the highest number that you can divide two integers who are both not zero and still return an integer. > We denote the greatest common divisor of two numbers as $gcd(a,b) \quad | a,b \in \mathbb{Z}$ >[!info]+ Read Time ⏱ **1 min** # Definition The greatest common divisor, greatest common factor or gcd is defined of two [[Integers]], which are not both zero, is the largest possible integer what can be divided. We often denote the gcd of two integers $a$ and $b$ as $gcd(a,b)$ We find the greatest common factor of two integers by writing out all divisible factors that allow the result to still be an integer. Our gcd of these two integers are the highest number of divisible number that both integers share ## Example Take for example $a = 18$ and $b = 24$, to find $gcd(a,b)$ we write out all the factors of $a$ and $b$. $ \begin{array}{c} \text{Factors of 18:}\quad 1,2,3,6,9,18 \\ \text{Factors of 24:} \quad 1,2,3,4,6,8,12,24 \\ gcd = 6 \end{array}$ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/jFd-6EPfnec?si=hqJSVqOC_IRHKMmJ" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidian-MathMatter) to support the project and help others discover it! ---