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Question
Find Greatest Common Divisor of 1111968 and 2963520, using prime factorization.
Answer
The GCD of given numbers is 864.
Explanation
Step 1 : Find prime factorization of each number.
1111968=2963520=2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅11⋅132⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅7⋅7⋅7(view steps on how to factor 1111968 and 2963520. )
Step 2 : Put a box around factors that are common for all numbers:
1111968=2963520=2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅11⋅132⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅7⋅7⋅7Step 3 : Multiply the boxed numbers together:
GCD=2⋅2⋅2⋅2⋅2⋅3⋅3⋅3=864
This solution can be visualized using a Venn diagram.
0,0
1111968
2963520
2
2
2
2
2
3
3
3
3
3
11
13
2
5
7
7
7
The GCD equals the product of the numbers at the intersection.
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