Question

Without performing actual division find the remainders left when $192837465$ is divided by $11$.

Answer 1

A number is said to be divisible by $11$ if the difference of the alternating sum of digits of is a multiple of 11

$192837465$

Sum of odd places$=1+2+3+4+5=15$

Sum of even places$=9+8+7+6=30$

$30-15=15$ when divided by $11$ we get remainder$=4$