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Divisibility by 7

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Is there any rule to check if a large number is divisible by 7? Like we can check for 2,3,5 etc
asked Feb 16, 2018 in Everything else by anonymous

1 Answer

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 Yes, there is a rule to check if a number is divisible by 7 without actually dividing it. It is, however, a little different than that of 2,3,5 etc. There are 2 rules. 

RULE 1:

  1. Remove the last digit 
  2. Double the last digit 
  3. Subtract it from the truncated original number (i.e. the original number without the last digit)
  4. Continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7.

EXAMPLE

Is 12264 divisible by 7 without leaving any remainder?

  • Remove the last digit:  1226
  • Double the last digit:    4 x 2 = 8
  • Subtract it:  1226 - 8 = 1218
  • Repeat the above steps 
    • 121 - 8 x 2
      •  = 121 - 16
      •  = 105
  • Repeat the above steps 
    • 10 - 5 x 2
      •  = 10 - 10
      •  = 0‚Äč

Since the final is 0, 12264 is divisible by 7

RULE 2:

  1. Take the digits of the number in reverse order
  2. Multiply them successively by the digits 1, 3, 2, 6, 4, 5
  3. Add the products
  4. If the resulting sum is divisible by 7, then the original number is divisible by 7
EXAMPLE
Is 12264 divisible by 7 without leaving any remainder?
  • Take the digits of the number in reverse order: 46221
  • Multiply them successively by the digits 1, 3, 2, 6, 4, 5:.... 4x1, 6x3, 2x2, 2x6, 1x4
  • Add the products: 4+18+4+12+4 = 42
  • 42 is divisible by 7, so 12264 is also divisible by 7
answered Feb 16, 2018 by anonymous
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