Final answer:
To find the greatest multiple of 36 using all ten digits, arrange the digits in descending order to form 987,654,312.
Step-by-step explanation:
To find the greatest multiple of 36 using all ten digits, we need to arrange the digits in descending order. The largest digit should be in the units place, the second-largest in the tens place, and so on. Since we can't use the digit 0, the largest multiple of 36 that can be formed is 987,654,312. This is the greatest multiple of 36 using all ten digits.