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BostonTC2018
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Is 1 a multiple of every number? Updated on: 23 Dec 2020, 11:57
Originally posted by BostonTC2018 on 23 Dec 2020, 11:52.
Last edited by BostonTC2018 on 23 Dec 2020, 11:57, edited 1 time in total.
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Hey! I got a question wrong for the below reason and was wondering if someone could help.

I assumed that "1" is a multiple of every integer and got this wrong because 7 was the lowest positive multiple.

I know that "0" is a multiple and it's not positive, so it couldn't be considered. Can someone explain to me the logic behind "1" not being an multiple of every #? Thank you!
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Is 1 a multiple of every number? 23 Dec 2020, 11:55
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MichaelFSchwarze
Hey!

I got this question wrong:

If n is a positive integer, is 1/n - 1/(n+1) < 1/20?
​​​
(1) n is odd

(2) n is a positive multiple of 7

I assumed that "1" is a multiple of every integer and got this wrong because 7 was the lowest positive multiple.

I know that "0" is a multiple and it's not positive, so it couldn't be considered. Can someone explain to me the logic behind "1" not being an multiple of every #? Thank you!
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This question is discussed here: https://gmatclub.com/forum/if-n-is-a-po ... 09268.html

1 is a factor (a divisor) of every integer, not a multiple of every integer.
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Is 1 a multiple of every number? 23 Dec 2020, 11:58
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Hey Bunuel - The previous post did not answer my specific question (i.e. is 1 a multiple of every #). Therefore, I'm going to leave this post up until someone answers that question. Appreciate the quick response though!

If you have any insights on if 1 is a multiple of every number, then would greatly appreciate it!
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Is 1 a multiple of every number? 23 Dec 2020, 12:00
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BostonTC2018
Hey Bunuel - The previous post did not answer my specific question (i.e. is 1 a multiple of every #). Therefore, I'm going to leave this post up until someone answers that question. Appreciate the quick response though!

If you have any insights on if 1 is a multiple of every number, then would greatly appreciate it!
Show more

I think I answered your question:

1 is a factor (a divisor) of every integer, not a multiple of every integer.
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Is 1 a multiple of every number? 23 Dec 2020, 12:32
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In order to be a “multiple” of some number, you must be divisible into that particular number of groups such that each group has the same (integer) number.
For example, 12 is a multiple of 6 because you can split 12 items into 6 groups such that each group has 2 (which is an integer) items.
0 is also a multiple of 6 because you can split 0 items into 6 groups such that each group has 0 (which is an integer) items.
If you have 1 item, can you split that item into some number of groups such that each groups has the same integer number of items? No, you can only “split” it into one group, meaning itself.

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Is 1 a multiple of every number? 22 Apr 2023, 17:34
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Wow! Awesome to stumble onto this post. Awesome to see the evolution of somebody going from a commonly confused concept of multiple and a factor (I had the same issue) to getting an admit at Harvard 😱


This proves that everyone has to start somewhere and your starting point does not determine your aunt point!


BostonTC2018
Hey! I got a question wrong for the below reason and was wondering if someone could help.

I assumed that "1" is a multiple of every integer and got this wrong because 7 was the lowest positive multiple.

I know that "0" is a multiple and it's not positive, so it couldn't be considered. Can someone explain to me the logic behind "1" not being an multiple of every #? Thank you!
Show more

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Is 1 a multiple of every number? 03 Jun 2024, 05:18
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