Does anyone know what the five digit number 5DDDD is when it is divisible by 6.
What is the digit D?
I have this so far...
50000/6 = 8333.33 remaining
51111/6 = 8518.5
52222/6 = 8703.66 remaining
53333/6 = 8888.83 remaining
54444/6 = 9074
55555/6 = 9259.166 remaining
56666/6 = 94444.33 remaining
Does this mean that 4 is the only digit of D that is divisible by 5DDD, because it is the only digits that goes into this problem evenly?
I honestly do not know if this is right...these are just my ideas. Any help or ideas would be greatly appreciated.
As undefined pointed out, an exhaustive search is a valid approach.
We can use some knowledge to aid in our search.
Since is divisible by 6, it is divisible by 2 and 3.
Since is divisible by 2, it must be an even number.
. . An even number ends in an even digit: 0, 2, 4, 6, or 8.
Since is divisible by 3, the sum of its digits must be a multiple of 3.
And we see that only is divisible by 6.
An integer is divisible by 6 if and only if it is divisible by 2 and it is divisible by 3.