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GCF - Greatest Common Factor











































the gcf of 9 and 20 is

The GCF (Greatest Common Factor) is the largest common factor of the two numbers (9 and 20).

It is the largest whole number that can be divided evenly into both the 9 and the 20.

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Sep 13, 2011
GCF - Greatest Common Factor
by: Staff


The question:

the gcf of 9 and 20 is



The answer:

The GCF (Greatest Common Factor) is the largest common factor of the two numbers.

To find the GCF, begin by listing all the factors of each number.

When a factor appears as a factor in both lists, it is a common factor.

The GCF is computed by multiplying all the common factors.

The factors for each of your two numbers are listed below:


20 = 1 x 2 x 2 x 5

9 = 1 x 3 x 3


There are no common factors except for the number “1”. Therefore, the greatest common factor is “1”.

So why does your teacher want you to know about the GCF?

There is a reason. You are learning a basic skill which you will need.

Although your math coursework has not covered this topic yet, in the future your ability to use the GCF will help you to factor complicated polynomial expressions such as 4x⁴+20x³+8x².


The GCF can also be used for practical, everyday problems.

For example, suppose you are buying square tiles for the floor of a room which measures 10 ft by 11 ft.

You don’t want to cut any of the tiles if you can avoid it.

What is the size of the largest whole, square tile that can be used to completely cover the floor?

To solve this problem, compute the Greatest Common Factor for the length and width of the room.

Length = 11 ft x 12 in per foot = 132 inches

Width = 10 ft x 12 in per foot = 120 inches

Factors of 132 = 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The GCF is 12.

The length of the largest square tile that can fit into this room is 12 in by 12 in.

You can use exactly 110 uncut tiles to cover the floor. No tile needs to be cut.



There is also a related concept your teacher may be leading up to:

LCM, least common multiple

The least common multiple (LCM) of two numbers is the smallest non-zero number that is a multiple of both.

To find the least common multiple of 9 and 20:

The multiples of 20 are:

1 * 20 = 20

2 * 20 = 40

3 * 20 = 60

4 * 20 = 80

5 * 20 = 100

6 * 20 = 120

7 * 20 = 140

8 * 20 = 160

9 * 20 = 180


The multiples of 9 are:

1 * 9 = 9

2 * 9 = 18

3 * 9 = 27

4 * 9 = 36

5 * 9 = 45

6 * 9 = 54

7 * 9 = 63

8 * 9 = 72

9 * 9 = 81

10 * 9 = 90

11 * 9 = 99

12 * 9 = 108

13 * 9 = 117

14 * 9 = 126

15 * 9 = 135

16 * 9 = 144

17 * 9 = 153

18 * 9 = 162

19 * 9 = 171

20 * 9 = 180

20 * 9 = 9 * 20 = 180

The least common multiple of the numbers 9 and 20 is: 180


Are there any practical uses for the LCM (least common multiple)?

Yes. I’m sure you are already familiar with one of the most important uses: adding or subtracting fractions with different denominators.

For example:

1/9 + 1/20

The LCM for 9 and 20 is 180.

The denominators of both fractions must be converted to the LCM of 180 before they can be added.

1/9 + 1/20

= (20/180) + (9/180)

= 29/180



Thanks for writing.

Staff
www.solving-math-problems.com


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