# Using divisibility test, determine whether 7138965 is divisible by 11 or not.

Answer

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Hint: Apply divisibility rule of 11 on the given number. If the given number satisfies the rule then it is divisible by 11 otherwise not. Take the alternating sum of digits in the number, read from left to right, if the resultant number is divisible by 11 then the given number is also divisible by 11.

Divisibility rule for 11: We have to find the sum of the digits in the even places and the sum of the digits in the odd places. If the difference between the two sums is 0 or a multiple of 11, then the given number would be divisible by 11. For example: we take any number like 72545.

Now, digits in odd places are 7, 5 and 5. Digits in even places are 2 and 4.

Now, sum of digits in the odd places \[=\text{ }7+5+5\text{ }=\text{ }17\]

And, sum of digits in the even places \[=\text{ }2+4=6\]

Therefore, taking the difference of these numbers, we get, \[17-6\text{ }=11\], which is divisible by 11. Therefore, the number 72545 is also divisible by 11.

Now, come to the question, the given number is 7138965.

Digits in odd places are 7, 3, 9 and 5 and the sum of these digits \[=\text{ }7+3+9+5\text{ }=\text{ }24\]. Digits in even places are 1, 8 and 6 and the sum of these digits\[=\text{ }1+8+6\text{ }=\text{ }15\].

Therefore, taking the difference of these numbers, we get,\[~24-15\text{ }=\text{ }9\] , which is not a multiple of 11, hence, 7138965 is not divisible by 11.

Note: If we would have done \[15-24\] then the result would have been\[-9\], which is also not divisible by 11. Hence, it does not matter how we take the difference, the result will be the same. So don’t think that the difference is taken so as to get a positive number.

__Complete step-by-step answer:__Divisibility rule for 11: We have to find the sum of the digits in the even places and the sum of the digits in the odd places. If the difference between the two sums is 0 or a multiple of 11, then the given number would be divisible by 11. For example: we take any number like 72545.

Now, digits in odd places are 7, 5 and 5. Digits in even places are 2 and 4.

Now, sum of digits in the odd places \[=\text{ }7+5+5\text{ }=\text{ }17\]

And, sum of digits in the even places \[=\text{ }2+4=6\]

Therefore, taking the difference of these numbers, we get, \[17-6\text{ }=11\], which is divisible by 11. Therefore, the number 72545 is also divisible by 11.

Now, come to the question, the given number is 7138965.

Digits in odd places are 7, 3, 9 and 5 and the sum of these digits \[=\text{ }7+3+9+5\text{ }=\text{ }24\]. Digits in even places are 1, 8 and 6 and the sum of these digits\[=\text{ }1+8+6\text{ }=\text{ }15\].

Therefore, taking the difference of these numbers, we get,\[~24-15\text{ }=\text{ }9\] , which is not a multiple of 11, hence, 7138965 is not divisible by 11.

Note: If we would have done \[15-24\] then the result would have been\[-9\], which is also not divisible by 11. Hence, it does not matter how we take the difference, the result will be the same. So don’t think that the difference is taken so as to get a positive number.

Last updated date: 31st May 2023

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