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Question
Find Greatest Common Divisor of 4666620000 and 4936617300, using prime factorization.
Answer
The GCD of given numbers is 3333300.
Explanation
Step 1 : Find prime factorization of each number.
4666620000=4936617300=2⋅2⋅2⋅2⋅2⋅3⋅5⋅5⋅5⋅5⋅7⋅41⋅2712⋅2⋅3⋅5⋅5⋅41⋅271⋅1481(view steps on how to factor 4666620000 and 4936617300. )
Step 2 : Put a box around factors that are common for all numbers:
4666620000=4936617300=2⋅2⋅2⋅2⋅2⋅3⋅5⋅5⋅5⋅5⋅7⋅41⋅2712⋅2⋅3⋅5⋅5⋅41⋅271⋅1481Step 3 : Multiply the boxed numbers together:
GCD=2⋅2⋅3⋅5⋅5⋅41⋅271=3333300
This solution can be visualized using a Venn diagram.
0,0
4666620000
4936617300
2
2
3
5
5
41
271
2
2
2
5
5
7
1481
The GCD equals the product of the numbers at the intersection.
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