Question

Without performing actual division, find the remainder when \[928174653\] is divided by 11.

Answer 1

Hint: We will add the odd numbers and even numbers given in the question separately and then find the difference in order to solve the answer. The difference will be divided by 11 and the answer will be the remainder asked by the question.

Complete step by step answer:
 Finding the sum of the odd numbers in the number \[928174653\] given in the question, we get-
$ \to 3 + 6 + 7 + 8 + 9 = 33$
Now, we will find the addition of even numbers in the numbers given in the question, we get-
$ \to 5 + 4 + 1 + 2 = 12$
Finding the difference between 33 and 12, in order to get a number to be divided by 11, we get-
$ \to 33 - 12 = 21$
Now, dividing 21 with 11. We will get the remainder asked in the question-
$ \to \dfrac{{21}}{{11}} = 10$
Thus, diving the number without performing actual division, we get the remainder = 10
Note: Such questions are easy but do not come to your mind that fast. Always find out the addition of the odd and even numbers. The difference when divided by the given digit in the question will give a remainder which will be your answer and if the number is completely divisible by 11 then the remainder will be Zero.