The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

To find the greatest number of four digits which is divisible by 15, 25, 40 and 75, we need to find the least common multiple (LCM) of these numbers first.

Step 1: Prime factorization of the numbers 15 = 3 * 5 25 = 5^2 40 = 2^3 * 5 75 = 3 * 5^2

Step 2: Find the LCM The LCM is the product of the highest powers of all the factors that appear in any of the numbers. So, LCM = 2^3 * 3 * 5^2 = 8 * 3 * 25 = 600

Step 3: Find the greatest 4-digit number divisible by the LCM The greatest 4-digit number is 9999. When we divide 9999 by 600, we get a quotient of 16 and a remainder of 399.

So, the greatest 4-digit number divisible by 600 is 9999 - 399 = 9600.

Therefore, the greatest number of four digits which is divisible by 15, 25, 40 and 75 is 9600.