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Intern
Status: That which doesn't break me, makes me stronger.
Joined: 27 Aug 2012
Posts: 19
Location: India
Concentration: Economics
GPA: 3.33
WE: Engineering (Consulting)
Followers: 0
Kudos [?]:
7
[0], given: 6
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Simple and quick divisibility test for 7 [#permalink]
 06 Feb 2013, 00:27
Here is something that I found while scratching my head and looking for the rules of divisibility for the number -7. Let's do it by example a) 2695 -Multiply the number of hundreds the number has by 2. 2695 = 2600 + 95 So, 26*2 = 52 -Add the remaining two digit number. Here the remaining two digit number is 95 Hence, 52+95 = 147 - Check whether the resulting sum is divisible by 7. if yes, then the original number is divisible by 7. 147/7 = integer Therefore, 2695 is divisible by 7 Another example: b) 26957 Step 1 => 26900 + 57 Therefore, 269*2 = 538 Step 2 => 538 + 57 = 595 Step 3 => Check if 595/7 is an integer. Indeed, 595/7 = 85 Thus, 26957 is divisible by 7. This in my opinion is the fastest way to check the divisibility of a number by 7.I'd be glad to see some appreciation in the form of Kudos.  
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Vishwa
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Director
Status: Disappointed devil..
Joined: 15 Sep 2012
Posts: 592
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Computer Software)
Followers: 20
Kudos [?]:
223
[0], given: 23
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Re: Simple and quick divisibility test for 7 [#permalink]
06 Feb 2013, 00:47
Quote: Step 1 => 26900 + 57
Therefore, 269*2 = 538
Step 2 => 538 + 57 = 595
Step 3 => Check if 595/7 is an integer. Indeed, 595/7 = 85
Actually looks a little tedious. 269*2, 595/7 , 538+57 one of these may be the exact point where things may go wrong. I follow a similar stratgey but with simple calculations involving 0s. It may or may not help others. Take out huge chunks from calculations that are multiple of 7. get help of 0s as much as possible  Such as, 28957 28000 is multiple of 7, so need to check only for 957 700 is multiple of 7, so need to check only for 257 210 is multiple of 7, so need to check only for 47 and we know the ans. Hope it helps
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Intern
Status: That which doesn't break me, makes me stronger.
Joined: 27 Aug 2012
Posts: 19
Location: India
Concentration: Economics
GPA: 3.33
WE: Engineering (Consulting)
Followers: 0
Kudos [?]:
7
[0], given: 6
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Re: Simple and quick divisibility test for 7 [#permalink]
06 Feb 2013, 00:58
Vips0000 wrote: Quote: Step 1 => 26900 + 57
Therefore, 269*2 = 538
Step 2 => 538 + 57 = 595
Step 3 => Check if 595/7 is an integer. Indeed, 595/7 = 85
Actually looks a little tedious. 269*2, 595/7 , 538+57 one of these may be the exact point where things may go wrong. I follow a similar stratgey but with simple calculations involving 0s. It may or may not help others. Take out huge chunks from calculations that are multiple of 7. get help of 0s as much as possible Such as, 28957 28000 is multiple of 7, so need to check only for 957 700 is multiple of 7, so need to check only for 257 210 is multiple of 7, so need to check only for 47 and we know the ans. Hope it helps You changed the number from 26957 to 28957, was it intentional? When the thousandth digits are multiple of 7 then, I'd go with your suggestion. I like it. However, when its not, as is the case here (26957), What will you do? 21000+5957 ? => 5600+357 => 350 + 7 => 7...! Hmmm, it may take same amount of time. I guess its a matter of preference. However, I like the suggestion. Will keep in mind.
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Thanks
Vishwa
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Director
Status: Disappointed devil..
Joined: 15 Sep 2012
Posts: 592
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Computer Software)
Followers: 20
Kudos [?]:
223
[0], given: 23
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Re: Simple and quick divisibility test for 7 [#permalink]
06 Feb 2013, 01:02
Vishwa25 wrote: You changed the number from 26957 to 28957, was it intentional? When the thousandth digits are multiple of 7 then, I'd go with your suggestion. I like it. However, when its not, as is the case here (26957), What will you do? 21000+5957 ? => 5600+357 => 350 + 7 => 7...! Hmmm, it may take same amount of time. I guess its a matter of preference. However, I like the suggestion. Will keep in mind. Intentional, to show the calculations. Quote: However, when its not, as is the case here (26957), What will you do? you can take your number: 26957 21000 is multiple of 7, so need to check only for 5957 5600 is multiple of 7, so need to check only for 357 350 is multiple of 7, so need to check only for 7 and we know the ans.
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Re: Simple and quick divisibility test for 7
[#permalink]
06 Feb 2013, 01:02
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