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Question
Find Greatest Common Divisor of 92610000 and 1372000, using prime factorization.
Answer
The GCD of given numbers is 686000.
Explanation
Step 1 : Find prime factorization of each number.
92610000=1372000=2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅5⋅5⋅5⋅7⋅7⋅72⋅2⋅2⋅2⋅2⋅5⋅5⋅5⋅7⋅7⋅7(view steps on how to factor 92610000 and 1372000. )
Step 2 : Put a box around factors that are common for all numbers:
92610000=1372000=2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅5⋅5⋅5⋅7⋅7⋅72⋅2⋅2⋅2⋅2⋅5⋅5⋅5⋅7⋅7⋅7Step 3 : Multiply the boxed numbers together:
GCD=2⋅2⋅2⋅2⋅5⋅5⋅5⋅7⋅7⋅7=686000
This solution can be visualized using a Venn diagram.
0,0
92610000
1372000
2
2
2
2
5
5
5
7
7
7
3
3
3
5
2
The GCD equals the product of the numbers at the intersection.
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