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

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siyer
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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   03 Nov 2010, 06:45
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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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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   03 Nov 2010, 07:15
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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.

Also on the 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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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   03 Nov 2010, 07:21
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Here is very similar information and broad answer.

https://www.manhattangmat.com/forums/num ... t4998.html
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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   03 Nov 2010, 07:21
Wow!! Thanks guys!
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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   03 Nov 2010, 07:56
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WOW. I got my first KUDOS!!!! Need many to get free tests.
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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   13 Mar 2014, 02:54
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.

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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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   13 Mar 2014, 03:17
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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.

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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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   05 Sep 2014, 04:16
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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.

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?
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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   05 Sep 2014, 04:47
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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.

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] New post   05 Sep 2014, 07:16
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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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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   14 Feb 2017, 23:54
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.

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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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   15 Feb 2017, 00:33
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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.

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] New post   31 Jul 2018, 19:48
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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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   31 Jul 2018, 20:47
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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] New post   19 Oct 2019, 11:48
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.
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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post   31 Dec 2023, 09:38
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