Question 1204671: 36, 48, 60 find the largest common factor of the numbers
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it look like 12 will be the largest common fqactor.
36/12 = 3
48/12 = 4
60/12 = 5
you are left with 3, 4, 5, which have no other common factors.
36, 48, 60 is equal to 12 * (3, 4, 5)
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is one elementary way of finding the greatest common factor, by finding the prime factorization of each number.
36 = 2*2*3*3
48 = 2*2*2*2*3
60 = 2*2*3*5
The greatest common factor is the product of all the primes that are common to all three numbers: 2*2*3 = 12.
And here is one of many other ways of finding the greatest common factor.
36 48 60
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Find any factor common to all three numbers; write that number on the left, and remove that common factor from each of the three numbers:
36 48 60
3 | 12 16 20
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Continue doing that until there are no more common factors in the three remaining numbers:
36 48 60
3 | 12 16 20
2 | 6 8 10
2 | 3 4 5
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The greatest common factor of the three numbers is the product of the common factors you have removed: 3*2*2 = 12.
Note this process also finds the least common multiple of the three numbers. It is the greatest common factor, times the numbers that remain: (3*2*2)*(3*4*5) = 12*60 = 720.
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