Find Greatest Common Divisor of 2024 and 1058, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}2024 =& 2\cdot2\cdot2\cdot11\cdot23\\[8pt]1058 =& 2\cdot23\cdot23\\[8pt]\end{aligned}$$

(view steps on how to factor 2024 and 1058. )

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

$$\begin{aligned}2024 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot11\cdot\color{red}{\boxed{23}}\\[8pt]1058 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{23}}\cdot23\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot23 = 46 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator