# algebra

posted by .

What is th remainder when the sum of the first 102 counting numbers is divided by 5220?

• algebra -

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.
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!

Try with 107*109, that should give 11663.

• algebra - oops -

Forgot to divide 10506 by 2 according to Gauss's rule:
10506/2=5253, divided by 5220 gives a quotient of 1 with 33 as a remainder, and divided by 5250 gives a quotient of 1 and 3 as a remainder.

• algebra -

i have no clue i am tring ti find the answer

## Similar Questions

1. ### algebra

The sum of the first n counting numbers 1 + 2 + 3 + 4 + 5 ... + n is given by S = n/2(1 + n). a) Find the sum of the numbers 14 to 40 inclusive Answer is 729. But i don't get why. Someone explain what the qestion means by "inclusive" …
2. ### algebra

The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. …
3. ### math

what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and …
4. ### Algebra

What is the remainder when the sum of the first 102 counting numbers is divided by 5250?
5. ### Algebra

Sorry Iposted that previous question wrong. Here is the right question. What is the remainder when the sum of the first 102 counting numbers is divided by 5250.
6. ### Math

How many integers bewteen 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
7. ### Math

How many integers between 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
8. ### Counting and Probability

What is the difference between the sum of the first 400 even counting numbers and the sum of the first 400 odd counting numbers?
9. ### Math

1. If the product of 5 and the sum of 10 and a certain number is equal to 15, what is the number?
10. ### maths

The sum of two consecutive counting numbers divided by their positive difference is 9. Find the larger numbers.

More Similar Questions