You can find the sum of the first 102 counting numbers using Gauss's method, namely:
"the sum of the first n counting numbers is n*(n+1)/2" whether n is odd or even.
For n = 102, the sum is 102*103/2=10506.
So divide 10506 by 5220 to get a quotient of 2, with a remainder of 66.
Mental calculation tip:
To multiply two numbers close to a hundred can be done in the head as follows, no paper, no calculators:
Let the numbers be (100+x) and (100+y), where x and y are small numbers. Take the example of 102 and 103, then x=2, y=3.
Start with the left most digit, which is a 1.
The next two digits are the sum of x and y, that gives 105.
The next two digits are the product of x and y, that gives 10506, et voilà!