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Math Help - Tests of Divisibility- Simple tricks

  1. #1
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    Tests of Divisibility- Simple tricks

    With this simple short cuts you can find out a number is divisible by a given number
    Divisible by 2: A number is divisible by 2, if its unitís digit is any of 0, 2, 4, 6, 8.
    Example: 6798512

    Divisible by 3: A number is divisible by 3, if sum of its digits divisible by 3.
    Example : 123456
    1+2+3+4+5+6 = 21
    21 is divisible by 3 so 123456 is also divisible by 3

    Divisible by 4: if the last two digits of a given are divisible 4, so the number can be divisible by 4.
    Example : 749232
    Last two digits are 32 which are divisible by 4 so the given number is also divisible by 4

    Divisible by 5: If unitís digit of a number is either Ď0í or Ď5í it is divisible 5.
    Example : 749230

    Divisible by 6: If a given number is divisible by 2 and 3 (which are factors of 6), then the number is divisible by 6.
    Example : 35256
    Unitís digit is 6 so divisible by 2
    3+5+2+5+6 = 21 so divisible by 3
    So 35256 divisible by 6

    Divisible by 8: if last 3 digits of a given number is divisible 8, then the given number is divisible 8.
    Example: 953360
    360 is divisible by 8, so 953360 is divisible by 8

    Divisible by 9: A number is divisible by 9, if sum of its digits divisible by 9.
    Example : 50832
    5+0+8+3+2 = 18 divisible by 9 so 50832 divisible by 9

    Divisible by 10: A number is divisible 10, if it ends with 0.
    Example : 508320

    Divisible by 11: A number is divisible by 11,if the difference of sum of its digits at odd places and sum of its digits at even places , is either 0 or a number divisible by 11.
    Example : 4832718
    (sum of digits at odd places ) Ė (sum of digits at even places)
    =(8+7+3+4)-(1+2+8) = 11 which is divisible by 11.
    So 4832718 is divisible by 11.

    I hope this simple tricks, will be very helpful to solve mathís homework problems easily.
    Thanks from topsquark
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  2. #2
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    Re: Tests of Divisibility- Simple tricks


    Divisible by 7

    Subtract twice the unit-digit from the 'rest of the number'.
    If the result is divisible by 7, the number is divisible by 7.

    Example: .Is 903 divisible ny 7?
    We have: . 90 - (2\cdot3) \:=\:84
    . . Since 84 is divisible by 7, then 903 is divisible by 7.


    The procedure can be repeated for larger numbers.

    Example: .Is 8813 divisible by 7?
    . . We have: . 881 - 6 \:=\:875
    Is 875 divisible by 7?
    . . We have: . 87-(2\cdot5) \:=\:77
    Since 77 is divisible by 7, then 8813 is divisible by 7.
    Thanks from topsquark and johng
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  3. #3
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    Re: Tests of Divisibility- Simple tricks

    Quote Originally Posted by Soroban View Post

    Divisible by 7

    Subtract twice the unit-digit from the 'rest of the number'.
    If the result is divisible by 7, the number is divisible by 7.

    Example: .Is 903 divisible ny 7?
    We have: . 90 - (2\cdot3) \:=\:84
    . . Since 84 is divisible by 7, then 903 is divisible by 7.


    The procedure can be repeated for larger numbers.

    Example: .Is 8813 divisible by 7?
    . . We have: . 881 - 6 \:=\:875
    Is 875 divisible by 7?
    . . We have: . 87-(2\cdot5) \:=\:77
    Since 77 is divisible by 7, then 8813 is divisible by 7.
    Thank you for this divisibility by 7 test
    Here is a quick proof

    (10x+d)-10(x-2d)=21d
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  4. #4
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    Re: Tests of Divisibility- Simple tricks

    Thanks for additional tips
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