Find Greatest Common Divisor of 42823 and 6409, using prime factorization.
Answer
The GCD of given numbers is 17.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}42823 =& 11\cdot17\cdot229\\[8pt]6409 =& 13\cdot17\cdot29\\[8pt]\end{aligned}$$(view steps on how to factor 42823 and 6409. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}42823 =& 11\cdot\color{blue}{\boxed{17}}\cdot229\\[8pt]6409 =& 13\cdot\color{blue}{\boxed{17}}\cdot29\\[8pt]\end{aligned}$$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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