What's the remainder

Algebra Level 2

$123456789123456789\ldots$ (up to 180 digits) when divided by 11 will have a remainder of:

6 5 4 0

2 solutions

Sahar Bano
Mar 13, 2020

According to divisible rule of 11 a number is divisible by 11 if and only if the difference of the sum of odd position digits and sum of even position digits is 0 or either divisible by 11

In the number there are 10 copies of 123456789123456789

It means the sum 1+3+5+7+9+2+4+6+8 is repeated 10 times and the same for 2+4+6+8+1+3+5+7+9

Therefore the difference of the sum of all odd position number and sum of all even position numbers is

=10[(1+3+5+7+9+2+4+6+8)-(2+4+6+8+1+3+5+7+9)] =10(0)=0

Therefore the number is divisible by 11

Hence the remainder is 0

Subhra Mukhopadhyay
Mar 28, 2014

123456789/11 -> reminders -> . 454545 (odd) 123456789123456789 / 11 reminders -> . 0 (even)

length of 1st string = 9 180/9 = 20 (even )

so reminder is 0 (zero)

A number is divisible by 11 if this is true:

1st Step: Starting from the one’s digit add every other digit

2nd Step: Add the remaining digits together

3rd Step:  Subtract 1st Step from the 2nd Step

*If this value is 0 then the number is divisible by 11. If it is not 0 then this is the remainder after dividing by 11 if it is positive. If the number is negative add 11 to it to get the remainder.

123456789123456789.... 180 digits we have (123456789123456789) 10 sets like this and by applying above rule for one set the difference is zero so the given number is divisible by 11

Satish Vootukuru - 7 years, 1 month ago

What's the remainder

2 solutions

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