Math Homework Help - GCF?

An easy technique is the prime factorization method, where you break down the numbers to their prime factors. I'll do the first, second and third problem.

1. GCF of 25, 75:

25 = 5 x 5
75 = 5 x 5 x 3

As you can see, there are two columns of 5. Consider each column as one number, so: 5 x 5 = 25

GCF is 25.
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2. GCF of 14, 21

14 = 7 x 2
21 = 7 x 3

Consider the column of 7 as one number. So the GCF is 7.
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3. GCF of 18, 57

18 = 3 x 3 x 2
57 = 3 x 19

Consider the column of three as one number, so the GCF is 3.
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4. GCF of 32, 24, 40

32 = 2 x 2 x 2 x 2 x 2
24 = 2 x 2 x 2 x 3
40 = 2 x 2 x 2 x 5

GCF is 2 x 2 x 2 = 8
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5. GCF of 25, 60, 75

25 = 5 x 5
60 = 5 x 2 x 2 x 3
75 = 5 x 5 x 3

GCF is 5.
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6. GCF of 12, 35, 15

12 = 3 x 2 x 2
35 = 5 x 7
15 = 5 x 3

GCF seems to be 1, since the three numbers don't share a common factor larger than 1.
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7. GCF of 15, 35, 20

15 = 3 x 5
35 = 7 x 5
20 = 2 x 5 x 2

GCF is 5.

To aid you in the other problems, here is a diagram on how to solve for the GCF. This comes in handy when handling large numbers.

http://i182.photobucket.com/albums/x144/pseudonyms_2007/Sample.jpg

Hope this helps.

1)
25 = .....5^2
75 = 3 x 5^2
--------------------------------
....= ......5^2
....= 25

2)
14 = 2 .....x 7
21 = .....3 x 7
--------------------------------
....= ...........7

3)
18 = 2 x 3^2
57 = ......3 x 19
--------------------------------
....= ......3

4)
32 = 2^5
24 = 2^3 x 3
40 = 2^3 x 5
--------------------------------
....= 2^3
....= 8

5)
25 = ..............5^2
60 = 2^2 x 3 x 5
75 = ........3 x 5^2
--------------------------------
....= ...............5

6)
12 = 2^2 x 3
35 = ...............5 x 7
15 = .........3 x 5
--------------------------------
....= 1

7)
15 = .........3 x 5
35 = ...............5 x 7
20 = 2^2 ......x 5
--------------------------------
....= ...............5

GCF of 25&75
factors of 25 = (1,5,25)
factors of 75 = (1,3,5,15.25.75)
common factors = (1,5,25)
GCF = 25

The GCF (greatest common factor) is the largest number that all numbers in the set can be divided by.... so for 25 and 75 = 25 because 1x25=25 and 3x25=75... Make sense?
14 and 21 = 7 (2x7=14 and 3x7=21)
18 and 57 = would be the number 1 because the only factors of 57 are 1 and 57. ...
32, 24, 40 = 8 (4x8=32, 3x8=24, 5x8=40)
25, 60, 75 = 5
12, 36, 15 = 3
15, 35, 20 = 5

1-----25
2------7
3------3
4------8
5------5
6--------Error in question at this one ?
7--------5

25
7
3
8
5
3
5
answer carefully.., gudluck!