Friday, November 9, 2012

Factors of a Number

The term factor of a number is a part in which a number can be broken down. All the factors of a number when multiplied together give the number. For example number 12; let us try with a factor tree, which helps in figuring out all different factors.

To Find the Factors of a Number 12, we can see that one is divisible by 12 so one is a factor. Then 2, 3,4 are too divisible so they all are factors of 12 too. We see if 5 is a factor or not, as 5 is not divisible by 12 so 5 is not a factor of 12. Then we take 6 and see the other numbers too. Hence we can conclude that All Factors of a Number 12 are 1, 2, 3, 4, 6 and 12.

Because these are also parts that can give us 12 so these are all numbers which can be considered as Factors of Number 12. Number one is the factor of all the numbers. From the algebra perspective we can see it this way, suppose we have x^2+3x . Let’s us understand by knowing first what do they have in common. So they both have an x, hence x is considered as a factor here.  And about the left overs, x times x is x ^2 and x times what is positive 3 after taking x as common, this equation can be written as X(x+3).

So we have factors not just in numbers but also in algebraic expressions in terms of variables. Factors are basically the numbers, which a larger number can get divided by.  Similarly if we have number, its factors will be 1, 3 and 9. We can find the Missing Factor by simply dividing the factor we know by the number we have. For example: - if we have number 15 and 1 and 5 are factors given to us.

To determine its missing factors, we can divide 15 by 5 which would give us 3. Hence 3 is also a factor. Therefore 1, 3, 5 and 15 are the factors of 15. Let us do one more example of finding the factors like what are the factors of number 8. As starting with the lowest number and its partner of course one times 8 gives us 8 only. Then 2, 4 and 8 are divisible by 8 too. Thus, 1,2,4,8 are all factors for number 8.

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