Find Greatest Common Divisor of 628 and 2260, using prime factorization.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}628 =& 2\cdot2\cdot157\\[8pt]2260 =& 2\cdot2\cdot5\cdot113\\[8pt]\end{aligned}$$(view steps on how to factor 628 and 2260. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}628 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot157\\[8pt]2260 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot5\cdot113\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot2 = 4 $$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