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.
Hello, matgrl!
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.
A positive integer is divisible by 3 if and only if its digital sum is divisible by 3. So you can actually repeat the digitial sum process iteratively (take the digital sum of the digital sum of the digital sum....) until you reach a single digit, if you wanted to.
An integer is divisible by 6 if and only if it is divisible by 2 and it is divisible by 3.