Find Greatest Common Divisor of 75 and 100, using prime factorization.
Answer
The GCD of given numbers is 25.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}75 =& 3\cdot5\cdot5\\[8pt]100 =& 2\cdot2\cdot5\cdot5\\[8pt]\end{aligned}$$(view steps on how to factor 75 and 100. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}75 =& 3\cdot\color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\\[8pt]100 =& 2\cdot2\cdot\color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 5\cdot5 = 25 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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