Find Greatest Common Divisor of 414 and 662, using prime factorization.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}414 =& 2\cdot3\cdot3\cdot23\\[8pt]662 =& 2\cdot331\\[8pt]\end{aligned}$$(view steps on how to factor 414 and 662. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}414 =& \color{blue}{\boxed{2}}\cdot3\cdot3\cdot23\\[8pt]662 =& \color{blue}{\boxed{2}}\cdot331\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
This page was created using
GCD Calculator