Question
Find Greatest Common Divisor of 250484713 and 250421789, using prime factorization.
Answer
The GCD of given numbers is 15731.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}250484713 =& 15731\cdot15923\\[8pt]250421789 =& 15731\cdot15919\\[8pt]\end{aligned}$$(view steps on how to factor 250484713 and 250421789. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}250484713 =& \color{blue}{\boxed{15731}}\cdot15923\\[8pt]250421789 =& \color{blue}{\boxed{15731}}\cdot15919\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 15731 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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