Question
Find Greatest Common Divisor of 205 and 1000, using prime factorization.
Answer
The GCD of given numbers is 5.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}205 =& 5\cdot41\\[8pt]1000 =& 2\cdot2\cdot2\cdot5\cdot5\cdot5\\[8pt]\end{aligned}$$(view steps on how to factor 205 and 1000. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}205 =& \color{blue}{\boxed{5}}\cdot41\\[8pt]1000 =& 2\cdot2\cdot2\cdot\color{blue}{\boxed{5}}\cdot5\cdot5\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 5 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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