Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the…

To find the greatest number N that divides 1305, 4665, and 6905, leaving the same remainder in each case, we follow a specific process: calculate the differences between the numbers and find their Highest Common Factor (H.C.F.).

Step-by-Step Calculation
1. Calculate the differences between the numbers:

Difference 1: 4665 - 1305 = 3360

Difference 2: 6905 - 4665 = 2240

Difference 3: 6905 - 1305 = 5600

2. Find the H.C.F. of the differences:
We need to find the H.C.F. of 3360, 2240, and 5600.

Dividing all by 10 gives: 336, 224, 560

Dividing all by 8 gives: 42, 28, 70

Dividing all by 14 gives: 3, 2, 5

Since 3, 2, and 5 have no common factors, the H.C.F. is 10 * 8 * 14 = 1120.

Therefore, the number N = 1120.

3. Find the sum of the digits in N:

N = 1120

Sum of digits = 1 + 1 + 2 + 0 = 4