Question
Find Greatest Common Divisor of 665 and 805, using prime factorization.
Answer
The GCD of given numbers is 35.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}665 =& 5\cdot7\cdot19\\[8pt]805 =& 5\cdot7\cdot23\\[8pt]\end{aligned}$$(view steps on how to factor 665 and 805. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}665 =& \color{blue}{\boxed{5}}\cdot\color{red}{\boxed{7}}\cdot19\\[8pt]805 =& \color{blue}{\boxed{5}}\cdot\color{red}{\boxed{7}}\cdot23\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 5\cdot7 = 35 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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