Dividing by eleven is fun

Number Theory Level 1

Which of the following numbers (given in decimal system) is divisible by 11?

363 249 111 933

Gary Ye by Gary Ye , 24, Austria

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9 solutions

Andrew Tiu
Dec 19, 2013

11's rule of divisibility states that if the sum of the even numbers minus sum of odd numbers equals 0 or is divisible by 11, it is divisible by 11. So 6 - (3 + 3) = 0.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

It is not sum of the even numbers minus sum of odd numbers

But difference of sum of digits at odd places and the sum of its digits at even places.

Sunil Pradhan - 7 years, 5 months ago
Ajesh K.C
Dec 19, 2013

if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then the number is divisible by 11.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

why the answer is 363 why no 121 also.

shaiq pervaiz - 7 years, 4 months ago

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There is no option as 121! It's 111

Prem Chebrolu - 3 years, 1 month ago

gr8

amir nazir - 7 years, 4 months ago

363; because 366/11=33.......

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Akhtar Malik
Dec 19, 2013

soln= 363/11=33

1 Helpful 0 Interesting 0 Brilliant 0 Confused

its so easy just divide 363 from 11

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Abhinav Ankur
Mar 22, 2014

The answer is 363

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Kajal Jain
Feb 27, 2014

if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then the number is divisible by 11.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Ya i solved in the same way..

prabha y n - 7 years, 2 months ago
Akhilesh Dixit
Jan 27, 2014

once we devied 363 by 11 than we will find 3 as a reminder and second time 33 will be devied by 3 time .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Without using long division, I found out that the middle term of 363 which is 6 which it is the sum of the first and last digit is 3 and 3 and this rule is applicable in divisibility rule of 11.

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