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# Everything you need to know about ‘0’ for GMAT

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Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 484

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04 Oct 2016, 22:13
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Everything you need to know about ‘0’ for GMAT

$$0$$ is an integer.
$$0$$ is an even integer.
$$0$$ is not Prime Number.
$$0$$ is not a natural number.
$$0$$ is the only number that is neither positive nor negative.
$$0$$ is the only number that is equal to its opposite; $$0=-0$$.

$$0$$ is multiple of every integer; $$0*2=0$$
$$0$$ is the FIRST multiple of any number but NOT the FIRST POSITIVE multiple.
$$0$$ is not a factor of any integer EXCEPT $$0$$. OG 208

$$\frac{a}{0}=$$ meaningless,undefined
$$\frac{0}{0}=$$ indeterminate
$$\frac{0}{a}=0$$

$$0$$ is a perfect square and also perfect cube.
$$0$$ is the only number that when raised to the zero power does not necessarily equal to 1; $$0^0≠1$$.

$$0^0$$ is indeterminate and never appear on the GMAT
$$0^n=0 (n\neq{0})$$
$$n^0=1 (n\neq{0})$$
$$0^0≠1$$

$$0!=1$$
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Hasan Mahmud
Retired Moderator
Joined: 27 Oct 2017
Posts: 1259
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

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10 Jan 2018, 08:43
is zero a factor of zero?

Mahmud6 wrote:
Everything you need to know about ‘0’ for GMAT

$$0$$ is an integer.
$$0$$ is an even integer.
$$0$$ is not Prime Number.
$$0$$ is not a natural number.
$$0$$ is the only number that is neither positive nor negative.
$$0$$ is the only number that is equal to its opposite; $$0=-0$$.

$$0$$ is multiple of every integer; $$0*2=0$$
$$0$$ is the FIRST multiple of any number but NOT the FIRST POSITIVE multiple.
$$0$$ is not a factor of any integer EXCEPT $$0$$. OG 208

$$\frac{a}{0}=$$ meaningless,undefined
$$\frac{0}{0}=$$ indeterminate
$$\frac{0}{a}=0$$

$$0$$ is a perfect square and also perfect cube.
$$0$$ is the only number that when raised to the zero power does not necessarily equal to 1; $$0^0≠1$$.

$$0^0$$ is indeterminate and never appear on the GMAT
$$0^n=0 (n\neq{0})$$
$$n^0=1 (n\neq{0})$$
$$0^0≠1$$

$$0!=1$$

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Retired Moderator
Joined: 27 Oct 2017
Posts: 1259
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

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10 Jan 2018, 08:51
1
@Mahmud6, "Please recheck your statement that zero is not a factor of any number except zero".

Zero is not a factor of anything, period. Look at it this way: for y to be a factor of x, you would check whether x/y = integer.
For example, 3 is a factor of 15 because 15/3 = 5, an integer. But n/0 = undefined, not an integer. Thus zero cannot be a factor of n, regardless of n's value. You cannot say that 0/0 = 0 just because zero is the numerator. The denominator of 0 makes 0/0 undefined.

https://www.manhattanprep.com/gmat/foru ... t4998.html

gmatbusters wrote:
is zero a factor of zero?

Mahmud6 wrote:
Everything you need to know about ‘0’ for GMAT

$$0$$ is an integer.
$$0$$ is an even integer.
$$0$$ is not Prime Number.
$$0$$ is not a natural number.
$$0$$ is the only number that is neither positive nor negative.
$$0$$ is the only number that is equal to its opposite; $$0=-0$$.

$$0$$ is multiple of every integer; $$0*2=0$$
$$0$$ is the FIRST multiple of any number but NOT the FIRST POSITIVE multiple.
$$0$$ is not a factor of any integer EXCEPT $$0$$. OG 208

$$\frac{a}{0}=$$ meaningless,undefined
$$\frac{0}{0}=$$ indeterminate
$$\frac{0}{a}=0$$

$$0$$ is a perfect square and also perfect cube.
$$0$$ is the only number that when raised to the zero power does not necessarily equal to 1; $$0^0≠1$$.

$$0^0$$ is indeterminate and never appear on the GMAT
$$0^n=0 (n\neq{0})$$
$$n^0=1 (n\neq{0})$$
$$0^0≠1$$

$$0!=1$$

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Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 484

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Updated on: 11 Dec 2018, 10:16
1
gmatbusters wrote:
@Mahmud6, "Please recheck your statement that zero is not a factor of any number except zero".

Zero is not a factor of anything, period. Look at it this way: for y to be a factor of x, you would check whether x/y = integer.
For example, 3 is a factor of 15 because 15/3 = 5, an integer. But n/0 = undefined, not an integer. Thus zero cannot be a factor of n, regardless of n's value. You cannot say that 0/0 = 0 just because zero is the numerator. The denominator of 0 makes 0/0 undefined.

https://www.manhattanprep.com/gmat/foru ... t4998.html

gmatbusters wrote:
is zero a factor of zero?

Mahmud6 wrote:
Everything you need to know about ‘0’ for GMAT

$$0$$ is an integer.
$$0$$ is an even integer.
$$0$$ is not Prime Number.
$$0$$ is not a natural number.
$$0$$ is the only number that is neither positive nor negative.
$$0$$ is the only number that is equal to its opposite; $$0=-0$$.

$$0$$ is multiple of every integer; $$0*2=0$$
$$0$$ is the FIRST multiple of any number but NOT the FIRST POSITIVE multiple.
$$0$$ is not a factor of any integer EXCEPT $$0$$. OG 208

$$\frac{a}{0}=$$ meaningless,undefined
$$\frac{0}{0}=$$ indeterminate
$$\frac{0}{a}=0$$

$$0$$ is a perfect square and also perfect cube.
$$0$$ is the only number that when raised to the zero power does not necessarily equal to 1; $$0^0≠1$$.

$$0^0$$ is indeterminate and never appear on the GMAT
$$0^n=0 (n\neq{0})$$
$$n^0=1 (n\neq{0})$$
$$0^0≠1$$

$$0!=1$$

Hi gmatbusters

Thank you for raising an important question. +1 Kudos to you.

Seeing your post, I initially thought I might be incorrect. Intriguing a little bit more I searched on google and found following two wonderful writings.

http://curiouscheetah.com/BlogMath/is-z ... r-of-zero/
http://mathforum.org/library/drmath/view/68272.html

I think the above two links will help to understand the matter more clearly.

P.S.: I am not a math nerd. These write-up use a lot of math jargons, most of which I could not understand but understood the conclusion 'zero is unambiguously a factor of zero'.
_________________
Hasan Mahmud

Originally posted by Mahmud6 on 11 Jan 2018, 00:00.
Last edited by Mahmud6 on 11 Dec 2018, 10:16, edited 1 time in total.
Retired Moderator
Joined: 27 Oct 2017
Posts: 1259
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

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12 Jan 2018, 06:12
Dear Sir
I am so thankful to you that you have tabulated a number of useful information about the most important integer, the ZERO INTEGER

As per official Quantitative review 2018, Factor/multiple is defined for non-zero integers.

so As far as GMAT is considered, zero is not a factor of any number including zero itself

Mahmud6 wrote:
Everything you need to know about ‘0’ for GMAT

$$0$$ is an integer.
$$0$$ is an even integer.
$$0$$ is not Prime Number.
$$0$$ is not a natural number.
$$0$$ is the only number that is neither positive nor negative.
$$0$$ is the only number that is equal to its opposite; $$0=-0$$.

$$0$$ is multiple of every integer; $$0*2=0$$
$$0$$ is the FIRST multiple of any number but NOT the FIRST POSITIVE multiple.
$$0$$ is not a factor of any integer EXCEPT $$0$$. OG 208

$$\frac{a}{0}=$$ meaningless,undefined
$$\frac{0}{0}=$$ indeterminate
$$\frac{0}{a}=0$$

$$0$$ is a perfect square and also perfect cube.
$$0$$ is the only number that when raised to the zero power does not necessarily equal to 1; $$0^0≠1$$.

$$0^0$$ is indeterminate and never appear on the GMAT
$$0^n=0 (n\neq{0})$$
$$n^0=1 (n\neq{0})$$
$$0^0≠1$$

$$0!=1$$
[/quote][/quote]
Hi gmatbusters

Thank you for raising an important question. +1 Kudos to you.

Seeing your post, I initially thought I might be incorrect. Intriguing a little bit more I searched on google and found following two wonderful writings.

http://curiouscheetah.com/BlogMath/is-z ... r-of-zero/
http://mathforum.org/library/drmath/view/68272.html

I think the above two links will help to understand the matter more clearly.

P.S.: I am not a math nerd. These write-ups use a lot of math jargons, most of which I could not understand but understood the conclusion 'zero is unambiguously a factor of zero'.[/quote]
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Re: Everything you need to know about ‘0’ for GMAT   [#permalink] 12 Jan 2018, 06:12
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