Find Greatest Common Divisor of 48 and 72, using Euclidean algorithm.
Answer
The GCD of given numbers is 24.
Explanation
Step 1 :
Divide $ 72 $ by $ 48 $ and get the remainder
The remainder is positive ($ 24 > 0 $), so we will continue with division.
Step 2 :
Divide $ 48 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 24 }} $.
We can summarize an algorithm into a following table.
| 72 | : | 48 | = | 1 | remainder ( 24 ) | ||
| 48 | : | 24 | = | 2 | remainder ( 0 ) | ||
| GCD = 24 | |||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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