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01 Aug 2022, 10:06
Kudos
Bookmarks
Hi,
Can an expert let me know if zero is a factor of itself.
If I am correct there are two ways to look at the definition of a factor and I am getting contradicting results by both (or I am terribly mistaken at the definition in itself - Either way, if the question sounds stupid, I apologize in advance
)
Definition 1
If a is a factor of b then b / a is an integer.
If I go by this definition, then 0 / 0 should be an integer, however anything divided by 0 is undefined.
Hence, my "logical" (or not so logical
) brain says that zero is NOT a factor of itself.
Definition 2
However, if I define factor as
If a is a factor of b then -
b= a * k (for some integer k)
By this definition, 0 seem to be a factor of itself.
In a nutshell, I am lost !
Can an expert help me out here and share his / her view on this.
Tagging few quant wizards to the thread, however anyone is welcome to share an opinion -
IanStewart chetan2u avigutman KarishmaB
Can an expert let me know if zero is a factor of itself.
If I am correct there are two ways to look at the definition of a factor and I am getting contradicting results by both (or I am terribly mistaken at the definition in itself - Either way, if the question sounds stupid, I apologize in advance
) Definition 1
If a is a factor of b then b / a is an integer.
If I go by this definition, then 0 / 0 should be an integer, however anything divided by 0 is undefined.
Hence, my "logical" (or not so logical
) brain says that zero is NOT a factor of itself.Definition 2
However, if I define factor as
If a is a factor of b then -
b= a * k (for some integer k)
By this definition, 0 seem to be a factor of itself.
In a nutshell, I am lost !
Can an expert help me out here and share his / her view on this.
Tagging few quant wizards to the thread, however anyone is welcome to share an opinion -
IanStewart chetan2u avigutman KarishmaB
avigutman
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GMAT 3: 770 Q50 V45
Expert reply
01 Aug 2022, 17:21
Kudos
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gmatophobia
Can an expert let me know if zero is a factor of itself.
Zero is not a factor of itself (though I've never had to know that on a GMAT question).gmatophobia
Definition 2
If a is a factor of b then -
b= a * k (for some integer k)
By this definition, 0 seem to be a factor of itself.
This definition does not imply that zero if a factor of itself. Please note the direction of your condition, gmatophobia. "If a is a factor of b then..." so you're presupposing that zero is a factor of itself. If it isn't, then the conditional clause is moot. If a is a factor of b then -
b= a * k (for some integer k)
By this definition, 0 seem to be a factor of itself.
01 Aug 2022, 19:53
Kudos
Bookmarks
gmatophobia
Hi,
Can an expert let me know if zero is a factor of itself.
If I am correct there are two ways to look at the definition of a factor and I am getting contradicting results by both (or I am terribly mistaken at the definition in itself - Either way, if the question sounds stupid, I apologize in advance )
Definition 1
If a is a factor of b then b / a is an integer.
If I go by this definition, then 0 / 0 should be an integer, however anything divided by 0 is undefined.
Hence, my "logical" (or not so logical ) brain says that zero is NOT a factor of itself.
Definition 2
However, if I define factor as
If a is a factor of b then -
b= a * k (for some integer k)
By this definition, 0 seem to be a factor of itself.
In a nutshell, I am lost !
Can an expert help me out here and share his / her view on this.
Tagging few quant wizards to the thread, however anyone is welcome to share an opinion -
IanStewart chetan2u avigutman KarishmaB
Can an expert let me know if zero is a factor of itself.
If I am correct there are two ways to look at the definition of a factor and I am getting contradicting results by both (or I am terribly mistaken at the definition in itself - Either way, if the question sounds stupid, I apologize in advance
) Definition 1
If a is a factor of b then b / a is an integer.
If I go by this definition, then 0 / 0 should be an integer, however anything divided by 0 is undefined.
Hence, my "logical" (or not so logical
) brain says that zero is NOT a factor of itself.Definition 2
However, if I define factor as
If a is a factor of b then -
b= a * k (for some integer k)
By this definition, 0 seem to be a factor of itself.
In a nutshell, I am lost !
Can an expert help me out here and share his / her view on this.
Tagging few quant wizards to the thread, however anyone is welcome to share an opinion -
IanStewart chetan2u avigutman KarishmaB
There is no universal agreement on this, some sources say that 0 is a factor of 0 while other sources say that 0 is not a factor of any number, including 0. In my opinion, 0 should be considered as a factor of 0. If you try to apply the first definition with a = 0, notice that you don't get some non-integer quotient, you get nothing at all. Do not make the mistake of thinking that there is a number called "undefined" lurking somewhere on the number line. There is not, it means that that operation is not defined. So you can't even use the first definition to test whether 0 is a factor of 0. On the other hand, you can define a factor as "a is called a factor of b if there exists some integer k such that b = a * k". You can apply this definition with a = b = 0 and the conclusion will be that 0 is a factor of 0. However, as I mentioned earlier, there is no general consensus on this issue. I don't think GMAT will ever give you a question where you need to know whether 0 is a factor of 0 to answer it.
