divide integer without remainder [closed]

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I have a set of numbers, where the total sum of them is always 1, I need to calculate the integer value that if divided on all those numbers the result will be without a remainder.



P.S: LCM won't work.



Any help?




elementary-number-theory




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closed as off-topic by amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner Aug 29 at 11:28


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.












  • This is about greatest common divisor rather than least common multiple.
    – hardmath
    Aug 28 at 13:17










  • GCD may be non integer, in my case I need an Integer
    – Eng7
    Aug 29 at 5:30










  • I don't follow your idea that the "GCD may be non integer". A common divisor of integers is an integer that divides them all. The GCD is simply the largest of those integer divisors.
    – hardmath
    Aug 29 at 17:07














up vote
0
down vote

favorite












I have a set of numbers, where the total sum of them is always 1, I need to calculate the integer value that if divided on all those numbers the result will be without a remainder.



P.S: LCM won't work.



Any help?




elementary-number-theory




share|cite|improve this question














closed as off-topic by amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner Aug 29 at 11:28


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.












  • This is about greatest common divisor rather than least common multiple.
    – hardmath
    Aug 28 at 13:17










  • GCD may be non integer, in my case I need an Integer
    – Eng7
    Aug 29 at 5:30










  • I don't follow your idea that the "GCD may be non integer". A common divisor of integers is an integer that divides them all. The GCD is simply the largest of those integer divisors.
    – hardmath
    Aug 29 at 17:07












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have a set of numbers, where the total sum of them is always 1, I need to calculate the integer value that if divided on all those numbers the result will be without a remainder.



P.S: LCM won't work.



Any help?




elementary-number-theory




share|cite|improve this question














I have a set of numbers, where the total sum of them is always 1, I need to calculate the integer value that if divided on all those numbers the result will be without a remainder.



P.S: LCM won't work.



Any help?





elementary-number-theory





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 28 at 13:18









hardmath

28.2k94693




28.2k94693










asked Aug 28 at 13:03









Eng7

1012




1012




closed as off-topic by amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner Aug 29 at 11:28


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner Aug 29 at 11:28


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, user91500, A. Goodier, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.











  • This is about greatest common divisor rather than least common multiple.
    – hardmath
    Aug 28 at 13:17










  • GCD may be non integer, in my case I need an Integer
    – Eng7
    Aug 29 at 5:30










  • I don't follow your idea that the "GCD may be non integer". A common divisor of integers is an integer that divides them all. The GCD is simply the largest of those integer divisors.
    – hardmath
    Aug 29 at 17:07
















  • This is about greatest common divisor rather than least common multiple.
    – hardmath
    Aug 28 at 13:17










  • GCD may be non integer, in my case I need an Integer
    – Eng7
    Aug 29 at 5:30










  • I don't follow your idea that the "GCD may be non integer". A common divisor of integers is an integer that divides them all. The GCD is simply the largest of those integer divisors.
    – hardmath
    Aug 29 at 17:07















This is about greatest common divisor rather than least common multiple.
– hardmath
Aug 28 at 13:17




This is about greatest common divisor rather than least common multiple.
– hardmath
Aug 28 at 13:17












GCD may be non integer, in my case I need an Integer
– Eng7
Aug 29 at 5:30




GCD may be non integer, in my case I need an Integer
– Eng7
Aug 29 at 5:30












I don't follow your idea that the "GCD may be non integer". A common divisor of integers is an integer that divides them all. The GCD is simply the largest of those integer divisors.
– hardmath
Aug 29 at 17:07




I don't follow your idea that the "GCD may be non integer". A common divisor of integers is an integer that divides them all. The GCD is simply the largest of those integer divisors.
– hardmath
Aug 29 at 17:07










1 Answer
1






active

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up vote
2
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I am going to assume "divided on" means "divided into". Suppose the sum of the numbers is $s$. If some integer $k$ divides each of the numbers without remainder then it must divide their sum without remainder too. So $s$ is a multiple of $k$. But we know $s=1$. So the only possible values for $k$ are $k= pm 1$.






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  • The question in other words, Integer/x should equal an integer, where x can be any number less or equal to 1. taking into consideration that I have not only x number, but multiple numbers their sum = 1 Ex: 0.25 , 0.5 and 0.25, in this case, 5 for example if divided on those numbers the result will be an integer without remainder.
    – Eng7
    Aug 28 at 13:17


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote













I am going to assume "divided on" means "divided into". Suppose the sum of the numbers is $s$. If some integer $k$ divides each of the numbers without remainder then it must divide their sum without remainder too. So $s$ is a multiple of $k$. But we know $s=1$. So the only possible values for $k$ are $k= pm 1$.






share|cite|improve this answer




















  • The question in other words, Integer/x should equal an integer, where x can be any number less or equal to 1. taking into consideration that I have not only x number, but multiple numbers their sum = 1 Ex: 0.25 , 0.5 and 0.25, in this case, 5 for example if divided on those numbers the result will be an integer without remainder.
    – Eng7
    Aug 28 at 13:17















up vote
2
down vote













I am going to assume "divided on" means "divided into". Suppose the sum of the numbers is $s$. If some integer $k$ divides each of the numbers without remainder then it must divide their sum without remainder too. So $s$ is a multiple of $k$. But we know $s=1$. So the only possible values for $k$ are $k= pm 1$.






share|cite|improve this answer




















  • The question in other words, Integer/x should equal an integer, where x can be any number less or equal to 1. taking into consideration that I have not only x number, but multiple numbers their sum = 1 Ex: 0.25 , 0.5 and 0.25, in this case, 5 for example if divided on those numbers the result will be an integer without remainder.
    – Eng7
    Aug 28 at 13:17













up vote
2
down vote










up vote
2
down vote









I am going to assume "divided on" means "divided into". Suppose the sum of the numbers is $s$. If some integer $k$ divides each of the numbers without remainder then it must divide their sum without remainder too. So $s$ is a multiple of $k$. But we know $s=1$. So the only possible values for $k$ are $k= pm 1$.






share|cite|improve this answer












I am going to assume "divided on" means "divided into". Suppose the sum of the numbers is $s$. If some integer $k$ divides each of the numbers without remainder then it must divide their sum without remainder too. So $s$ is a multiple of $k$. But we know $s=1$. So the only possible values for $k$ are $k= pm 1$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 28 at 13:13









gandalf61

6,061522




6,061522











  • The question in other words, Integer/x should equal an integer, where x can be any number less or equal to 1. taking into consideration that I have not only x number, but multiple numbers their sum = 1 Ex: 0.25 , 0.5 and 0.25, in this case, 5 for example if divided on those numbers the result will be an integer without remainder.
    – Eng7
    Aug 28 at 13:17

















  • The question in other words, Integer/x should equal an integer, where x can be any number less or equal to 1. taking into consideration that I have not only x number, but multiple numbers their sum = 1 Ex: 0.25 , 0.5 and 0.25, in this case, 5 for example if divided on those numbers the result will be an integer without remainder.
    – Eng7
    Aug 28 at 13:17
















The question in other words, Integer/x should equal an integer, where x can be any number less or equal to 1. taking into consideration that I have not only x number, but multiple numbers their sum = 1 Ex: 0.25 , 0.5 and 0.25, in this case, 5 for example if divided on those numbers the result will be an integer without remainder.
– Eng7
Aug 28 at 13:17





The question in other words, Integer/x should equal an integer, where x can be any number less or equal to 1. taking into consideration that I have not only x number, but multiple numbers their sum = 1 Ex: 0.25 , 0.5 and 0.25, in this case, 5 for example if divided on those numbers the result will be an integer without remainder.
– Eng7
Aug 28 at 13:17



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