Three number are in the ratio of 2: 3 : 5 and their L.C.M. is 2400. Their H.C.F. is:

To find the H.C.F. (Highest Common Factor), we first need to find the actual numbers that are in the ratio 2:3:5.

Step 1: We know that the L.C.M. (Least Common Multiple) of these numbers is 2400. The L.C.M. is obtained by multiplying the numbers by their H.C.F.

So, let's assume the H.C.F. is 'h'. Then the numbers will be 2h, 3h, and 5h.

Step 2: The L.C.M. of 2h, 3h, and 5h is the product of these numbers, which is 30h^2.

Step 3: We know that the L.C.M. is 2400. So, we can set up the equation 30h^2 = 2400.

Step 4: Solving this equation for 'h', we get h^2 = 2400/30 = 80.

Step 5: Taking the square root of both sides, we find that h = sqrt(80) = 8.94 (approximately).

So, the H.C.F. of these numbers is approximately 8.94.