Question

Find the three digits numbers which are divisible by 11

Answer 1

110 , 121,142,153,164,175,186,197 and many more

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Answer 2

First three-digit number that is divisible by 11 = 110

Next number = 110 + 11 = 121

Therefore, 110, 121, 132, …

All are three digit numbers which are divisible by 11 and thus, all these are terms of an A.P. having first term as 110 and common difference as 11.

The maximum possible three-digit number is 999. When we divide it by 11, the remainder will be 9. Clearly, 999 − 9 = 990 is the maximum possible three-digit number that is divisible by 11.

The series is as follows.

110, 121, 132, … 990

Let 990 be the nth term of this A.P.

a = 110

d = 11

an = 990

n = ?

an = a + (n − 1) d

990 = 110 + (n − 1) 11

880 = (n − 1) 11

(n − 1) = 80

n = 81

Therefore, 81 three-digit numbers are divisible by 11.

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