Find the difference of the largest and smallast numbers formed by using all the digits 0,5,6,7,8 with no digit used twice.

the largest number is 87650

the smallest number, assuming we don't start with a zero, is 50678
and their difference is ......

To find the difference between the largest and smallest numbers formed by using all the digits 0, 5, 6, 7, 8 without using any digit twice, follow these steps:

1. Arrange the digits in ascending order: 0, 5, 6, 7, 8.
2. The smallest number will begin with the digit 0, so place 0 in the leftmost position.
3. The largest number will begin with the largest available digit, which is 8. Therefore, place 8 in the rightmost position.
4. We now have the numbers 0 _ _ _ 8. There are three remaining digits to be placed in the three remaining positions.
5. To maximize the value, place the next largest available digit, which is 7, in the second position from the left.
6. We now have the numbers 0 7 _ _ 8. There are two remaining digits and two remaining positions.
7. Place 6 in the third position from the left and 5 in the remaining position to obtain the largest number: 0 7 6 5 8.
8. To find the smallest number, reverse the digits: 8 5 6 7 0.

Therefore, the largest number is 07658, and the smallest number is 85670. To find the difference between them, subtract the smallest number from the largest number: 07658 - 85670 = -78012.
The difference between the largest and smallest numbers formed by using all the digits 0, 5, 6, 7, 8 without using any digit twice is -78012.