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Question 220141: What is a common factor? Where do you use the common factor in an expression consisting of various terms?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A common factor is a factor that applies to multiple terms.
Suppose you have number 1 and 3
The only common factor between these two number is 1.
1//1 = 1
3/1 = 3
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As a point in fact, though, we do not consider the number 1 as a common factor because all number can be divided by 1.
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We look for common factors greater than 1.
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Take the numbers 2 and 4
A common factor is 2 because:
2/2 = 1
4/2 = 2
Both number can be divided by 2 and yield an integer result.
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Integer result is another requirement, since all numbers can be divided by another number smaller than them and yield an answer if the answer does not have to be an integer.
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Common factors for 7 and 5 are?????
There are none becauswe there is no number than can be divided evenly into 7 and 5 at the same time. Matter of fact, there is no number smaller than these number and greater than 1 that can be divided into each of these numbers by itself because these numbers are prime numbers.
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Take 9 and 3
3 goes evenly into 9 and 3 goes evenly into 3 so 3 is a common factor of 3 and 9.
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Common factors are used to manipulate terms and expressions so they can be solved easier.
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We can use them to simplify division.
Take the case of:
5*10*7*3*9 / 5*7*3
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We have a common factor of 5 in the numerator that will cancel out a 5 in the denominator. Similarly with 7 and 3.
Out equation reduces to:
10*9 which equals 90.
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Using the common factor helped reduce the equation so it could be solved easier.
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We can use it to simplify multiplication.
Take the case of 5*7 + 3*7 + 6*7
We have a common factor of 7 that can change this equation to:
7 * (5+3+6) which equals 7 * 14 which equals 98
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Using the common factor helped reduce the equation so it coulde be solved easier.
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Look at x^ + 2x + 1 / (x+1)
The numerator in this equation can be factored to equals (x+1)^2
This changes our equation to:
(x+1)^2 / (x+1) which becomes ( (x+1) * (x+1) ) / (x+1)
Take out the common factor of (x+1) from the numberator and denominator and you are left with:
x+1
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It's true this equation could also have been solved by dividing (x+1) into x^2 + 2x + 1 as follows:
equation of x^2+2x+1 divided by (x+1) = x with a remainder of x+1
remainder of x+1 divided by (x+1) = 1 with no more remainder.
Solution is x+1
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We got the same answer but we have to work harder to get it. Recognizing the common factor made solution of the problem easier.
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