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Manager  Joined: 15 Apr 2010
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Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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siyer wrote:
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?

An integer $$a$$ is a multiple of an integer $$b$$ means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Hope it helps.
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Here is very similar information and broad answer.

http://www.manhattangmat.com/forums/num ... t4998.html
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Manager  Joined: 15 Apr 2010
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Wow!! Thanks guys!
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Senior Manager  Joined: 25 May 2010
Posts: 287
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GMAT 1: 590 Q47 V25 GMAT 2: 560 Q47 V20 GMAT 3: 600 Q47 V25 GMAT 4: 680 Q49 V34 Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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WOW. I got my first KUDOS!!!! Need many to get free tests.
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Bunuel wrote:
siyer wrote:
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?

An integer $$a$$ is a multiple of an integer $$b$$ means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Hope it helps.

Dear Bunuel,

And the first factor of any number(>=0) is 1. am I right?

thanks
Sid
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Joined: 02 Sep 2009
Posts: 58434
Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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sidpopy wrote:
Bunuel wrote:
siyer wrote:
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?

An integer $$a$$ is a multiple of an integer $$b$$ means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Hope it helps.

Dear Bunuel,

And the first factor of any number(>=0) is 1. am I right?

thanks
Sid

Yes, the smallest factor, the smallest positive divisor of any positive integer is 1.
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Bunuel wrote:
siyer wrote:
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?

An integer $$a$$ is a multiple of an integer $$b$$ means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Hope it helps.

Hi,
Then why LCM of two numbers not zero?
Math Expert V
Joined: 02 Sep 2009
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Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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tushain wrote:
Bunuel wrote:
siyer wrote:
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?

An integer $$a$$ is a multiple of an integer $$b$$ means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Hope it helps.

Hi,
Then why LCM of two numbers not zero?

By definition the lowest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b.
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Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Quote:
By definition the lowest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b.

Thanks Bunuel
One more doubt: Can LCM, HCF be stated for -ve numbers: for eg. what is the LCM of -36,-12 or HCF of -12,+36 ?
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Bunuel wrote:
siyer wrote:
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?

An integer $$a$$ is a multiple of an integer $$b$$ means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Hope it helps.

Dear Bunuel, Does zero (0) consider as consecutive even integers? (0)(2)(4)(6)(8)
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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ziyuenlau wrote:
Bunuel wrote:
siyer wrote:
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?

Do we consider 0 to be a multiple of every number?

An integer $$a$$ is a multiple of an integer $$b$$ means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Hope it helps.

Dear Bunuel, Does zero (0) consider as consecutive even integers? (0)(2)(4)(6)(8)

0 is an even integer, so it can be a part of the sequence of even numbers.
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Hi Bunuel ,

A quick one.

Suppose a=4.5, b=1.5; a/b would still be an integer.
So unless mentioned in the question about the nature of "a" and "b", shouldn't we consider fractions as well for Data Sufficiency questions?

Really appreciate your time!

Cheers,
Sushil
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Joined: 02 Sep 2009
Posts: 58434
Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Sushil_Sali15 wrote:
Hi Bunuel ,

A quick one.

Suppose a=4.5, b=1.5; a/b would still be an integer.
So unless mentioned in the question about the nature of "a" and "b", shouldn't we consider fractions as well for Data Sufficiency questions?

Really appreciate your time!

Cheers,
Sushil

Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only).

So, a proper GMAT question won't tell you that a is divisible by b without saying that a and b are positive integers.
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Re: Is 0 (zero) to be considered as a multiple of every number?  [#permalink]

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Zero can not be counted as a multiple of all numbers.
Simple explanation is here:

Consider 0 as a multiple of 5 and a multiple of 7.
Then LCM(5,7)=0
Which is obviously wrong.

I have another explanation too.
But I guess this is enough. Re: Is 0 (zero) to be considered as a multiple of every number?   [#permalink] 19 Oct 2019, 11:48
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