Find Greatest Common Divisor of 446492299 and 186378511, using prime factorization.
Answer
The GCD of given numbers is 11.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}446492299 =& 11\cdot11\cdot53\cdot69623\\[8pt]186378511 =& 11\cdot16943501\\[8pt]\end{aligned}$$(view steps on how to factor 446492299 and 186378511. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}446492299 =& \color{blue}{\boxed{11}}\cdot11\cdot53\cdot69623\\[8pt]186378511 =& \color{blue}{\boxed{11}}\cdot16943501\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 11 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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