Question
Find Greatest Common Divisor of 667 and 29000, using prime factorization.
Answer
The GCD of given numbers is 29.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}667 =& 23\cdot29\\[8pt]29000 =& 2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot29\\[8pt]\end{aligned}$$(view steps on how to factor 667 and 29000. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}667 =& 23\cdot\color{blue}{\boxed{29}}\\[8pt]29000 =& 2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot\color{blue}{\boxed{29}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 29 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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