Find Greatest Common Divisor of 2024 and 572, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}2024 =& 2\cdot2\cdot2\cdot11\cdot23\\[8pt]572 =& 2\cdot2\cdot11\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 2024 and 572. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}2024 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot\color{Fuchsia}{\boxed{11}}\cdot23\\[8pt]572 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{11}}\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot11 = 44 $$

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator