Question
Find Greatest Common Divisor of 7939 and 437325, using prime factorization.
Answer
The GCD of given numbers is 17.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}7939 =& 17\cdot467\\[8pt]437325 =& 3\cdot5\cdot5\cdot7\cdot7\cdot7\cdot17\\[8pt]\end{aligned}$$(view steps on how to factor 7939 and 437325. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}7939 =& \color{blue}{\boxed{17}}\cdot467\\[8pt]437325 =& 3\cdot5\cdot5\cdot7\cdot7\cdot7\cdot\color{blue}{\boxed{17}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 17 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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