Check if a number is divisible by 3

Question

I need to find whether a number is divisible by 3 without using %, / or *. The hint given was to use atoi() function. Any

Answer 1

A number divisible by 3, iirc has a characteristic that the sum of its digit is divisible by 3. For example,

12 -> 1 + 2 = 3
144 -> 1 + 4 + 4 = 9

Answer 2

• Here is a pseudo-algol i came up with .

Let us follow binary progress of multiples of 3

000 011
000 110

001 001
001 100
001 111

010 010
010 101


011 000
011 011
011 110

100 001
100 100
100 111

101 010
101 101

just have a remark that, for a binary multiple of 3 x=abcdef in following couples abc=(000,011),(001,100),(010,101) cde doest change , hence, my proposed algorithm:

divisible(x):

    y = x&7

    z = x>>3

    if number_of_bits(z)<4

        if z=000 or 011 or 110 , return (y==000 or 011 or 110) end

        if z=001 or 100 or 111 , return (y==001 or 100 or 111) end

        if z=010 or 101 , return (y==010 or 101) end

    end

    if divisible(z) , return (y==000 or 011 or 110) end

    if divisible(z-1) , return (y==001 or 100 or 111) end

    if divisible(z-2) , return (y==010 or 101) end

end

Answer 3

The interview question essentially asks you to come up with (or have already known) the divisibility rule shorthand with 3 as the divisor.

One of the divisibility rule for 3 is as follows:

Take any number and add together each digit in the number. Then take that sum and determine if it is divisible by 3 (repeating the same procedure as necessary). If the final number is divisible by 3, then the original number is divisible by 3.

Example:

16,499,205,854,376
=> 1+6+4+9+9+2+0+5+8+5+4+3+7+6 sums to 69
=> 6 + 9 = 15 => 1 + 5 = 6, which is clearly divisible by 3.

See also

• Wikipedia/Divisibility rule - has many rules for many divisors

Answer 4

well a number is divisible by 3 if all the sum of digits of the number are divisible by 3. so you could get each digit as a substring of the input number and then add them up. you then would repeat this process until there is only a single digit result.

if this is 3, 6 or 9 the number is divisable by 3.