Find Greatest Common Divisor of 3552 and 2208, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}3552 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot37\\[8pt]2208 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot23\\[8pt]\end{aligned}$$

(view steps on how to factor 3552 and 2208. )

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

$$\begin{aligned}3552 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot\color{blue}{\boxed{3}}\cdot37\\[8pt]2208 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot\color{blue}{\boxed{3}}\cdot23\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot2\cdot3 = 96 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator