Largest Number Dividing 245 and 1029 with Remainder 5

Finding the Common Divisor
To find the largest number that divides 245 and 1029 by leaving a remainder of 5 in each case, we need to find the common divisor of the two numbers.

Calculating the Remainder
When 245 is divided by this common divisor, it leaves a remainder of 5. Similarly, when 1029 is divided by the same common divisor, it also leaves a remainder of 5.

Using Euclidean Algorithm
We can use the Euclidean algorithm to find the greatest common divisor of 245 and 1029. This algorithm involves finding the remainder of the division of the larger number by the smaller number and then repeating the process with the smaller number and the remainder until the remainder is 0.

Applying the Euclidean Algorithm
245 ÷ 1029 = 0 with a remainder of 245
1029 ÷ 245 = 4 with a remainder of 29
245 ÷ 29 = 8 with a remainder of 5
29 ÷ 5 = 5 with a remainder of 4
5 ÷ 4 = 1 with a remainder of 1
4 ÷ 1 = 4 with a remainder of 0

Result
The greatest common divisor of 245 and 1029 is 5. Therefore, the largest number that divides 245 and 1029 by leaving a remainder of 5 in each case is 5.