Question

Without performing actual division, find the remainder left when 192837465 is divided by 11.

Answer 1

Hint: Here, 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:
According to our question it is asked to us that without performing actual division find the remainders left when 192837465 is divided by 11.
Finding the sum of odd numbers in the number 192837465 given in the question we get –
\[\Rightarrow 5+4+3+2+1=15\]
Now, we will find the addition of even numbers in the numbers given in the question, we get –
\[\Rightarrow 9+8+7+6=30\]
Find the difference between 15 and 30, in order to get a number to be divided by 11, we get,
\[\Rightarrow 30-15=15\]
Now, dividing 15 with 11. We will get the remainder asked in the question \[\Rightarrow \dfrac{15}{11}=4\].
Thus, dividing the number without performing actual division, we get the remainder \[=4\].

Note: Always find out the addition of odd and even numbers. The difference when divided by the given digits 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.