Answer: 987654301
Step-by-step explanation:
The factors of 6 are 2 and 3:
2*3 = 6.
So we want a big number that is no divisible by 2 or 3.
Then:
The number can not end in 0, 2, 4, 6 or 8.
The addition of the digits can not add to a multiple of 3.
If we want to construct the largest number possible, we should try to use the largest number at the beginning, so we have:
9876543210
but we can not end in 0, so we can write this as:
9876543201
but 9 + 8 +7 + 6 +5 + 3 + 2 + 1 = 45, it is a multiple of 3, so we should discard one of these numbers, lets discard the 1, as it is the smaller one.
we can write:
987654203 but if instead we remove the 2, we can leave the 3 in the place and get:
987654301 that is bigger, it ends with an odd number so it is not a multiple of 2, and the addition of all the digits adds up to 44, so this is not a multiple of 3.
Then this is the answer,
