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# Is 0 (zero) to be considered as a multiple of every number?

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Manager
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Is 0 (zero) to be considered as a multiple of every number? [#permalink]  03 Nov 2010, 05:45
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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]  03 Nov 2010, 06:15
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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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Senior Manager
Joined: 25 May 2010
Posts: 321
Location: United States
Concentration: Strategy, Finance
Schools: CBS '14 (A)
GMAT 1: 590 Q47 V25
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GMAT 3: 600 Q47 V25
GMAT 4: 680 Q49 V34
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Kudos [?]: 50 [1] , given: 32

Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink]  03 Nov 2010, 06:21
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http://www.manhattangmat.com/forums/num ... t4998.html
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Manager
Joined: 15 Apr 2010
Posts: 176
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Kudos [?]: 72 [0], given: 25

Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink]  03 Nov 2010, 06:21
Wow!! Thanks guys!
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Senior Manager
Joined: 25 May 2010
Posts: 321
Location: United States
Concentration: Strategy, Finance
Schools: CBS '14 (A)
GMAT 1: 590 Q47 V25
GMAT 2: 560 Q47 V20
GMAT 3: 600 Q47 V25
GMAT 4: 680 Q49 V34
Followers: 4

Kudos [?]: 50 [0], given: 32

Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink]  03 Nov 2010, 06:56
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]  13 Mar 2014, 01:54
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: 28780
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Kudos [?]: 47330 [0], given: 7121

Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink]  13 Mar 2014, 02:17
Expert's post
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]  05 Sep 2014, 03:16
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
Joined: 02 Sep 2009
Posts: 28780
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Kudos [?]: 47330 [0], given: 7121

Is 0 (zero) to be considered as a multiple of every number? [#permalink]  05 Sep 2014, 03:47
Expert's post
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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Joined: 17 Mar 2014
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Is 0 (zero) to be considered as a multiple of every number? [#permalink]  05 Sep 2014, 06:16
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 ?
Is 0 (zero) to be considered as a multiple of every number?   [#permalink] 05 Sep 2014, 06:16
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