What is the remainder when 120! is divided by 12024?

The remainder when 120! is divided by 12024 is 0.

Here's why:

The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n. So, 120! is the product of all positive integers from 1 to 120.

The number 12024 is divisible by several numbers that are less than or equal to 120, including 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 162, 216, 324, 648, and several others.

Since 120! is the product of all positive integers from 1 to 120, it is divisible by all of these factors of 12024. Therefore, when 120! is divided by 12024, the remainder is 0.