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21 May 2010, 10:17
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We all know the rules for 2,3,4,5,6,8,9 and 10. But what is less talked about is the number 7.
Here is the shortcut to see whether the number is divisible by 7 or not.
Step1: Take a number and multiply each of the digit beginning on the right hand side by 1,3,2,6,4,5 (repeat the pattern if the number is large enough)
Step 2: Add the product of the numbers. If the sum is divisible by 7 -- so is the number.
e.g. Check for number 133
3(1) + 3(3) + 1(2) = 14 --> which is divisible by 7. So, 133 is divisible by 7.
Another example: check for no. 2016
6(1) + 1(3) + 0(2) + 2(6) = 21 --> which is also divisible by 7. So, the no. 2016 is divisible by 7.
Here is the shortcut to see whether the number is divisible by 7 or not.
Step1: Take a number and multiply each of the digit beginning on the right hand side by 1,3,2,6,4,5 (repeat the pattern if the number is large enough)
Step 2: Add the product of the numbers. If the sum is divisible by 7 -- so is the number.
e.g. Check for number 133
3(1) + 3(3) + 1(2) = 14 --> which is divisible by 7. So, 133 is divisible by 7.
Another example: check for no. 2016
6(1) + 1(3) + 0(2) + 2(6) = 21 --> which is also divisible by 7. So, the no. 2016 is divisible by 7.
21 May 2010, 11:24
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Here's another one:
1. Lop off the last digit of the number in question. For 2016, that would be 6.
2. Double that number. Double the 6 to get 12.
3. Subtract that number from the remaining digits of the number in question, as if they were a stand-alone number. So you don't subtract 12 from 2016, or from 2010. You subtract 12 from 201 to get 189.
4. Repeat steps 1-3 until you get to a number you recognize as either a multiple of 7 or not. If you get a multiple of 7 after step 3, the original number was a multiple of 7. If you get a non-multiple of 7 after step 3, the original number was not a multiple of 7.
Take 189, lop of the 9, double to get 18, and subtract 18 from the 18 we got when we took 9 off the end of 189. Result 0 is divisible by 7, so 2016 also was.
Another example: 13,587
1. Separate: 1358 and 7
2. Double the 7: 14
3. Subtract: 1358-14 = 1344
1. Separate: 134 and 4
2. Double the 4: 8
3. Subtract: 134-8 = 126
Recognize 126 as 14 less than 140, i.e. a multiple of 7.
Conclusion: 13,587 is a multiple of 7.
1. Lop off the last digit of the number in question. For 2016, that would be 6.
2. Double that number. Double the 6 to get 12.
3. Subtract that number from the remaining digits of the number in question, as if they were a stand-alone number. So you don't subtract 12 from 2016, or from 2010. You subtract 12 from 201 to get 189.
4. Repeat steps 1-3 until you get to a number you recognize as either a multiple of 7 or not. If you get a multiple of 7 after step 3, the original number was a multiple of 7. If you get a non-multiple of 7 after step 3, the original number was not a multiple of 7.
Take 189, lop of the 9, double to get 18, and subtract 18 from the 18 we got when we took 9 off the end of 189. Result 0 is divisible by 7, so 2016 also was.
Another example: 13,587
1. Separate: 1358 and 7
2. Double the 7: 14
3. Subtract: 1358-14 = 1344
1. Separate: 134 and 4
2. Double the 4: 8
3. Subtract: 134-8 = 126
Recognize 126 as 14 less than 140, i.e. a multiple of 7.
Conclusion: 13,587 is a multiple of 7.
General Discussion
21 May 2010, 11:16
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That is totally weird. I can't be bothered to check if it's true (I assume it is)... I'd love to see the proof as to why it works. Not because I'm that big of a math geek, but because I'm sure it would boggle my mind even further. 
