Find Greatest Common Divisor of 403, 465 and 651, using prime factorization.
Answer
The GCD of given numbers is 31.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}403 =& 13\cdot31\\[8pt]465 =& 3\cdot5\cdot31\\[8pt]651 =& 3\cdot7\cdot31\\[8pt]\end{aligned}$$(view steps on how to factor 403, 465 and 651. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}403 =& 13\cdot\color{blue}{\boxed{31}}\\[8pt]465 =& 3\cdot5\cdot\color{blue}{\boxed{31}}\\[8pt]651 =& 3\cdot7\cdot\color{blue}{\boxed{31}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 31 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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