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Is 0 (zero) to be considered as 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, 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] New post 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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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post 03 Nov 2010, 06:21
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Here is very similar information and broad answer.

http://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, 06:21
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, 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] New post 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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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post 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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post 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?
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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post 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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Is 0 (zero) to be considered as a multiple of every number? [#permalink] New post 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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