Find Greatest Common Divisor of 204 and 255, using prime factorization.
Answer
The GCD of given numbers is 51.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}204 =& 2\cdot2\cdot3\cdot17\\[8pt]255 =& 3\cdot5\cdot17\\[8pt]\end{aligned}$$(view steps on how to factor 204 and 255. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}204 =& 2\cdot2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{17}}\\[8pt]255 =& \color{blue}{\boxed{3}}\cdot5\cdot\color{red}{\boxed{17}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 3\cdot17 = 51 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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