Find the biggest multiple of 36, which consists of all 10 digits, each used once.

The biggest multiple of 36, which consists of all 10 digits, each used once 8754321096.

Explanation:

Conditions for a number to be completely divisible by 36,

last 2 digits should be divisible by 4 the sum of the digits of the number should be divisible by 9.

When we add the digits of the numbers 0 to 9, we get 45, which is divisible by 9.

Similarly, the greatest 2-digit number that is divisble by 4 is 96

So the last 2 positions of the 10-digit number can be 96.

Filling the rest of the positions by the numbers in descending order, we get the greatest multiple of 36 with all the 10 digits used only once to be 8754321096.