Question
Find Greatest Common Divisor of 1561 and 3409, using prime factorization.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1561 =& 7\cdot223\\[8pt]3409 =& 7\cdot487\\[8pt]\end{aligned}$$(view steps on how to factor 1561 and 3409. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1561 =& \color{blue}{\boxed{7}}\cdot223\\[8pt]3409 =& \color{blue}{\boxed{7}}\cdot487\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 7 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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