To find the greatest 4-digit number that is exactly divisible by both 45 and 60, we need to find the largest multiple of the least common multiple (LCM) of 45 and 60 within the range of 4-digit numbers.
LCM of 45 and 60 = 180
Now, divide 9999 (the largest 4-digit number) by 180:
9999 ÷ 180 = 55 with a remainder of 99
So, the largest multiple of 180 within the range of 4-digit numbers is 55 * 180 = 9900. Therefore, the greatest 4-digit number divisible by both 45 and 60 is 9900.