Factors and Multiples.........

[Taran]

Hi,

I was going through Factors and Multiples theory and am stuck with a doubt. Here it is....

Multiple:
Multiples of X are obtained by multiplying X with any whole number - agreed i.e multiples of x are 0, X, 2X, 3X...so on
Multiples are infinite - agreed
Value of Multiple of X is >= X - Not agreed (X multiplied by any whole number could give us zero as well, which is less than X). I also read somewhere that ZERO IS A MULTIPLE OF ANY INTEGER. How is this possible?

Please explain.........

Taran

[Rahul@gurome]

...
Value of Multiple of X is >= X - Not agreed (X multiplied by any whole number could give us zero as well, which is less than X). I also read somewhere that ZERO IS A MULTIPLE OF ANY INTEGER. How is this possible?
...

Yes, you are correct.
This is not possible. Not only because of zero, also because of negative multiples (Such as -14 is a multiple of 7).

[Taran]

Thanks Rahul,

But i do not understand. I read this from Manhattan Number Property Guide. It now feels that my number prop prep is taking a huge hit........plz help.

You are also correct that we can have -ve integers when multiplied by whole numbers will yield 0 or -ve integers. But then these -ve multiples will be either equal to original -ve integer or smaller than it. This again spoils the fun of the definition that Manhattan has given. ............. please help me as to how to proceed learning these things.

Another question - How can i find factors of -ve integers? For example, -12 = -1 x 2^2 x 3.....How many factors here??? and what???

Thanks for ur help...

Taraan

[Rahul@gurome]

In general and in GMAT, when considering factors of a positive integer, we only consider the positive factors. But truly speaking negative factors are factors too.

Say, if we are asked to find the factors of 12, we will only consider 1, 2, 3, 4, 6 and 12.
But if we are asked whether -2 or -4 or -6 is a factor of 12 or not, the answer is yes.

This sounds confusing but this is how it works.


However for negative integer, this is less ambiguous.
While determining factors of a negative integer, we can consider the positive as well as the negative factors too. For example,

Another question - How can i find factors of -ve integers? For example, -12 = -1 x 2^2 x 3.....How many factors here??? and what???

Factors of -12 are -12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6 and 12.