Find Greatest Common Divisor of 685, 192 and 189, using prime factorization.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}685 =& 5\cdot137\\[8pt]192 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\\[8pt]189 =& 3\cdot3\cdot3\cdot7\\[8pt]\end{aligned}$$(view steps on how to factor 685, 192 and 189. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}685 =& 5\cdot137\\[8pt]192 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\\[8pt]189 =& 3\cdot3\cdot3\cdot7\\[8pt]\end{aligned}$$Note that in this example numbers do not have any common factors.
Step 3 : Multiply the boxed numbers together:
Since there is no boxed numbers we conclude that $~\color{blue}{ \text{GCD = 1} } $.
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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