Find Greatest Common Divisor of 20 and 45, using prime factorization.
Answer
The GCD of given numbers is 5.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}20 =& 2\cdot2\cdot5\\[8pt]45 =& 3\cdot3\cdot5\\[8pt]\end{aligned}$$(view steps on how to factor 20 and 45. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}20 =& 2\cdot2\cdot\color{blue}{\boxed{5}}\\[8pt]45 =& 3\cdot3\cdot\color{blue}{\boxed{5}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 5 $$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