Final answer:
The greatest multiple of 36 that uses all 10 digits is 9876543201.
Step-by-step explanation:
To find the greatest multiple of 36 that uses all 10 digits, we need to find a number that is divisible by 36 and contains all the digits 0-9. Since 36 is divisible by 9 (which is the sum of digits from 0 to 9), any multiple of 36 that contains all the digits 0-9 will also be divisible by 9. Therefore, we can start by finding the greatest multiple of 36 that is divisible by 9 and contains all the digits 0-9. The largest such number is 9876543201, which is a multiple of both 36 and 9.