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Question
Find Greatest Common Divisor of 8925 and 76576500, using prime factorization.
Answer
The GCD of given numbers is 8925.
Explanation
Step 1 : Find prime factorization of each number.
8925=76576500=3⋅5⋅5⋅7⋅172⋅2⋅3⋅3⋅5⋅5⋅5⋅7⋅11⋅13⋅17(view steps on how to factor 8925 and 76576500. )
Step 2 : Put a box around factors that are common for all numbers:
8925=76576500=3⋅5⋅5⋅7⋅172⋅2⋅3⋅3⋅5⋅5⋅5⋅7⋅11⋅13⋅17Step 3 : Multiply the boxed numbers together:
GCD=3⋅5⋅5⋅7⋅17=8925
This solution can be visualized using a Venn diagram.
0,0
8925
76576500
3
5
5
7
17
2
2
3
5
11
13
The GCD equals the product of the numbers at the intersection.
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