Question
Find Greatest Common Divisor of 602 and 1505, using prime factorization.
Answer
The GCD of given numbers is 301.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}602 =& 2\cdot7\cdot43\\[8pt]1505 =& 5\cdot7\cdot43\\[8pt]\end{aligned}$$(view steps on how to factor 602 and 1505. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}602 =& 2\cdot\color{blue}{\boxed{7}}\cdot\color{red}{\boxed{43}}\\[8pt]1505 =& 5\cdot\color{blue}{\boxed{7}}\cdot\color{red}{\boxed{43}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 7\cdot43 = 301 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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