Every natural number from 1 to 2010 is divided by 7 each leaving a remainder between 0 and 6 what is the sum of these remainders?

Answer 1

For the first seven numbers:

1 / 7 gives a remainder of 1

2 / 7 gives a remainder of 2

3 / 7 gives a remainder of 3

4 / 7 gives a remainder of 4

5 / 7 gives a remainder of 5

6 / 7 gives a remainder of 6

7 / 7 gives a remainder of 0

... for a total of 21.

After this, the pattern repeats. So, you need to find the closest multiple of seven that is less than 2010, see how many "cycles" you have there, multiply the number of cycles by 21, then separate calculate the remainder for the last few numbers.