Find Greatest Common Divisor of 1001 and 910, using prime factorization.
Answer
The GCD of given numbers is 91.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1001 =& 7\cdot11\cdot13\\[8pt]910 =& 2\cdot5\cdot7\cdot13\\[8pt]\end{aligned}$$(view steps on how to factor 1001 and 910. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1001 =& \color{blue}{\boxed{7}}\cdot11\cdot\color{red}{\boxed{13}}\\[8pt]910 =& 2\cdot5\cdot\color{blue}{\boxed{7}}\cdot\color{red}{\boxed{13}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 7\cdot13 = 91 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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