Sum of Three Digit Numbers leaving Remainder 3 when Divided by 5

Explanation:
To find the sum of all three-digit natural numbers which leave a remainder of 3 when divided by 5, we need to follow a systematic approach.

Finding the Range:
- The smallest three-digit number is 100, and the largest three-digit number is 999.
- We need to find the numbers in this range that leave a remainder of 3 when divided by 5.

Finding the Numbers:
- To find the numbers that leave a remainder of 3 when divided by 5, we can start by looking at the first few numbers: 103, 108, 113, 118, ...
- We can observe a pattern that repeats every 5 numbers.
- So, we need to find how many groups of 5 numbers exist within the range of three-digit numbers.

Calculating the Sum:
- To find the sum, we can calculate the average of the first and last number in each group of 5, as they are equally spaced.
- The average of the first and last number in each group is (103+118)/2 = 110.5.
- There are 180 groups of 5 numbers in the range of three-digit numbers.
- So, the sum of all three-digit numbers leaving a remainder of 3 when divided by 5 is 180 x 110.5 = 19935.
Therefore, the sum of all three-digit natural numbers which leave a remainder of 3 when divided by 5 is 19935.